Aalto, Alvar

, 173, 259

Aalto-Musiktheater Essen

, 112

Baker House

, 113, 131, 218

Church of the Three Crosses

, 123

Finlandia Hall

, 104–105

Helsinki house

, 216

Leverkusen Cultural Center

, 231–232

Maison Louis Carré

, 77

Mount Angel Benedictine College

, 121

Neue Vahr apartments

, 122

Otaniemi Technical University (Aalto University)

, 67, 161

Paimio Sanitorium

, 16–17, 188

Rovaniemi Library

, 121, 122

Säynätsalo Town Hall

, 21, 22, 160, 253, 254

Seinäjoki Library

, 121, 122

Shiraz Art Museum

, 113–114, 233–234

Viipuri Library

, 111, 192, 250–251

Wolfsburg Cultural Center

, 52, 113

Aalto-Musiktheater Essen

, 112

Abbey of Fontenay

, 24, 26, 232

Accommodation, deformative

, 252–259

single spiral via

, 253, 254

Acropolis, Athens

, 257–259

Addition

, 3, 13–40, 263

adjoining

, 14, 53, 228

collidive embedding

, 26–29

embedding

, 232–234

encapsulation

, 32–33, 240

enfacing

, 24–26, 230–232

linear linking

, 15–17, 228–229

matrix embedding

, 17–21, 29

superposition

, 30–32, 234–239

taxonomy of

, 39, 40

touching

, 21–23, 229–230

“Z axis” cases

, 29, 33–39, 236, 240–244

Adhesion

, 112

Adjaye, David

, 15

Adjoining

, 14, 53, 228

planar form of dimensionalities

, 129

Aesthetics

, 2

Ahmedabad Mill Owners’ Association Building

, 152–153

AIA

Headquarters

, 80

NC Center for Architecture and Design

, 154

Alianza Arquitectos

Kress residence

, 47

Aligned partial penumbras

core-centered

, 217–220

void-centered

, 221–223

Aligned partial radial arrays

, 178–179

void-centered

, 185–187

Aligned partial shell arrays

core-centered

, 191–192

void-centered

, 194–195

Aligned single shells

core-centered aligned partial penumbras

, 217–220

void-centered aligned partial penumbras

, 222

Allegheny County Courthouse

, 77–78, 137

Alternative readings

, 30

Altes Museum

, 23, 24

Amagansett parents’ house

, 142–143

American Heritage Center

, 12

Ames, Anthony

Villa Chang

, 30, 31

Andrews, John

Harvard University’s Gund Hall

, 88

Scarborough College

, 252–253, 259

Annie Maxim House

, 115

Apple Headquarters

, 209

Arc de Triomphe de l’Étoile

, 193

Arc de Triomphe du Carrousel

, 193

Arche de la Défense

, 8

Arquitectonica

Atlantis Condominium

, 84–85, 87

Mandell Residences

, 221

North Dade Justice Center

, 34, 35

Overseas Tower

, 135

Palace Condominium

, 31, 32, 131

Spear house

, 195

Asplund, Erik Gunnar

Lister County Courthouse

, 212

Stockholm Public Library

, 23, 24, 155–156, 157

Villa Snellman

, 22, 23

AT&T Long Lines

, 182, 183

Atlanta Hyatt Regency

, 78

Atlantis Condominium

, 84–85, 87, 222

“Babel IIB,” hypothetical design

, 71–72

Baker House

, 113, 131, 164, 218

Bangladesh Assembly Building

, 207

Bangladesh National Assembly House

, 251

Barcelona Pavilion

, 149–150

Barnes, Edward Larrabee

Crown Center Office Complex

, 54, 55, 158, 159

Haystack Mountain School of Crafts

, 180, 181

Kittredge Dormitories

, 160, 182, 183

Barnes Foundation

, 147, 256, 257

Barry, Donna

Stevie Ellis Dance Theater

, 156–157, 158

Barton house

, 32

Bauhaus Building

, 158–159, 253

Bavinger house

, 117

Belleview Square

, 175

Bending deformation

, 131

plastic bending

, 113–115

plastic failure

, 115–116

rigid failure

, 116

Ben Gurion Airport Tel Aviv

, 174

Bermuda house

, 26–28, 213

Biomorphic deformation

, 118–121

Biomuseo

, 153–154

Blobitecture

, 119

Blumenthal house

, 26, 213

Bo & Wohlert

Louisiana Museum

, 236

Bohlin Cywinski Jackson

Gaffney house

, 190

Ledge House

, 213–214, 215

Luzerne County Community College Conference Center

, 138, 184

Bohlin Powell Larkin Cywinski

Shelly Ridge Girl Scout Center’s Activity Lodge

, 76

Boissonnas House

, 65, 66

Borgund’s Stave Church

, 58, 105, 190

Borromini

Palazzo Spada

, 52

Boston

Long Wharf Hotel

, 89

Boston City Hall

, 37–38, 39, 82, 151–152, 208, 209

Bosworth, Willliam Welles

MIT’s Maclaurin Buildings

, 178, 179

Botta, Mario

Ligornetto House

, 222

Posteria Residence

, 91

Boullée

, 9

Brant House

, 104

Braun Headquarters

, 139–140

Breuer, Marcel

Whitney Museum of American Art

, 87–88

Broadway

, 246

Bryant Park

, 246

Buckwalter House

, 51, 52, 56–58

Burj Khalifa

, 59

Byker Wall

, 131, 136

Cabrillo Marine Museum

, 19, 20, 29

California Aerospace Museum

, 29, 30

Cambridge’s Johnson house

, 157, 158

Cambridge History Faculty Building

, 79

Cambridge University’s Harvey Court

, 158

Carlin, Earl

Mount Zion Seventh-Day Adventist Church

, 60, 61

Carpenter Center for the Visual Arts, Harvard University

, 42–43, 44, 161–162, 242, 243

Catalano, Eduardo

Catalano house

, 132, 151

Cayan Tower

, 118

CCTV Headquarters

, 94

Cellular mitosis

, 41

Centerbrook

Crowell house

, 211

Centering

, 1–4, 170

arrays

, 173–197

hybrids

, 227–259

modes of

, 264–272

mode transformation ring

, 273

Centrifugal force

, 13

Centripetal force

, 13

Chalgren, Jean

Arc de Triomphe de l’Étoile

, 224–225

Cheney house

, 203–204

Christ Church Spitalfields

, 61, 62

Chrysler Building

, 144, 145

The Church Incarnate: The Sacred Function of Christian Architecture

, 275

Church of the Three Crosses

, 123

Cincinnati’s Federated building

, 80, 81, 96

Cité de Refuge

, 135

Citicorp Center

, 89, 90

City of Palmanova, Italy

, 234–235

City of Refuge, Paris

, 234

Clark & Menefee

Inn at Middleton Place

, 154, 155, 217

Clements/Rumpel

School of Architecture Building, Florida A&M University

, 230–231

Cobb, Henry

John Hancock Tower

, 110

Portland Museum of Art

, 52–53

Cohesion

, 31

College Life Insurance Company

, 66, 67

Collidive embedding

addition

, 26–29

Columbus Fire Station

, 138

Compressive deformation

, 105, 107–109, 114

Connecticut private residence

, 206

Cook & Fournier

Kunsthaus Graz

, 119

Coop Himmelb(l)au

Dalian International Conference Center

, 120, 240

Core-centered aligned partial penumbras

aligned incremented radial arrays

, 217

aligned single shells

, 217–220

linking

, 220

sequence of

, 217

Core-centered full penumbras

incremented radial arrays

, 200–202

linking

, 204–207

sequence of

, 201

single shells

, 202–204

Core-centered partial penumbras

incremented radial arrays

, 210–211

linking

, 212–213

partial single shells

, 211–212

sequence of

, 210

Core-centered radials

aligned partial radial arrays

, 178–179

full radial arrays

, 174–176

partial radial arrays

, 177–178

sequence of

, 174

single radials

, 179–181

Core-centered shells

, 188–193

aligned partial shell arrays

, 191–192

full shell arrays

, 189–191

incremental shell arrays

, 192–193

partial shell arrays

, 191

Core-centered unitary redux

, 225

Cores

, 245

Cornell University Undergraduate Housing

, 137

Corner-to-corner relationships

, 22, 23

Cossuta, Araldo

Long Wharf Marriott Hotel

, 89, 90, 137, 179, 180

Cour Carrée du Louvre

, 193

Couvent Sainte Marie de La Tourette

, 165–167, 255–256

Crowell house

, 211

Crown Center Office Complex

, 54, 55, 158, 159

Cummins Occupational Health Center

, 30, 31

Dalian International Conference Center

, 120, 240

Dana House

, 18, 202

David & Gladys Wright House

, 117, 118

Deformation

, 100, 103, 126, 143, 158, 262

bending

, 113–116, 131

biomorphic

, 118–121

compressive

, 105, 107–109, 114

deformative accommodation

, 252–259

explosive

, 121–125

implosive

, 125–126

morphing

, 251–252

shear

, 109–113

tensile forces

, 104–107, 263

torque

, 117–118

Desert Nomad House

, 14

de Young Museum

, 147–148, 256–257

Dhaka Assembly Building

, 23, 25

Die-cutting

, 87, 91

Die Stijl

, 130

Diller & Scofidio

Eyebeam Musuem of Art & Technology

, 114

Lake Neuchatel’s Blur Building

, 101

Dimensionalities

, 3, 127–140, 271

linear form of

, 135–137

planar form of

, 128–133

planar/linear form of

, 139

volumetric/linear form of

, 137–138

volumetric/planar form of

, 133–135

+

volumetric/planar/linear form of

, 139–140

Directional deformation

, 121–123

Dodecahedron

, 8

Dominican Motherhouse

, 229

“Door-within-a-door-within-a-door-within-a-door,”

, 49

Douglas House

, 43, 44, 214

Dreier-Barton house

, 46, 47, 49

Ductility

, 105

Duplication

evolution of

, 56, 64

linear

, 47–48

planar

, 65–68, 246

singular

, 41–44, 106

volumetric

, 64, 71–72

Eastern State Penitentiary, Philadelphia

, 174

East Wing, National Gallery, Washington, D.C.

, 205, 235

Edge-centered subtraction

elevation-oriented (three dimension)

, 92–93

elevation-oriented (two dimension)

, 85–86

plan-oriented (one dimension)

, 76–77

plan-oriented (two dimension)

, 78–79

Edwin Cheney house

, 190

Einstein Tower

, 118, 119, 122

Eisenman, Peter

City of Culture of Galicia

, 100

House VI (Frank house)

, 154–155

House X

, 44, 155, 156

Wexner Center

, 182–183

Elasticity

, 105

Elevation-oriented subtraction

one dimension

, 82–84

three dimension

, 91–96

two dimension

, 84–91

types of

, 83

Embankment

, 87

Embedding

, 232–234

collidive

, 26–29

core-centered full penumbras

, 205–206

core-centered partial penumbras

, 212–213

matrix

, 17–21, 29

Empire State Building

, 144

Encapsulation

, 41, 46–47, 135, 240

in additive sequence of expansion

, 32–33

core-centered full penumbras

, 206

Endless House

, 148, 149

Enfacing

, 65, 134, 230–232

addition

, 24–26

Erdman Hall Dormitories

, 47, 244, 245

Erechtheion

, 258

Erik Boissonnas house II

, 134

Erosion

, 59, 80, 96–97

Erosive toothing

, 77

Erskine, Ralph

Byker Wall

, 131

European Arcades

, 75–76

Everson Museum of Art

, 43, 45, 85, 86, 251, 252

Ewha Womans University

, 100

Explosive deformation

, 121–125

Extrusion

, 87

Eyebeam Musuem of Art & Technology

, 114

Face-centered subtraction

elevation-oriented (one dimension)

, 82–84

elevation-oriented (three dimension)

, 92

elevation-oriented (two dimension)

, 84–91

plan-oriented (one dimension)

, 75–76

plan-oriented (three dimension)

, 81–82

plan-oriented (two dimension)

, 77–78

Failure

plastic

, 115–116

rigid

, 116

shear

, 111–113, 192

tensile

, 105–107

Fallingwater

, 59–61, 214, 254, 255

Farnsworth house

, 36, 37, 128, 129

“Field plowing” sequences

, 266

Fifth Avenue Apple Store

, 101

Finlandia Hall

, 104–105

Fire Station 4, Columbus

, 212

Floating

, 244

Florey Building, Oxford University

, 216

Florida A&M University

School of Architecture Building

, 230–231

Fondation Cartier

, 129, 194, 195

Ford Foundation Building, Manhattan

, 212, 213

Formability

, 105

Formative hybrids

, 141–170

linear

, 158–160

planar

, 149–152

planar/linear

, 162–163

volumetric

, 142–148

volumetric/linear

, 160–162

volumetric/planar

, 152–157

volumetric/planar/linear

, 163–170

Forming

, 1–4, 41, 227

modes of

, 262–263, 269–272

Forum of Pompeii

, 232

Foster, Norman

Apple Headquarters

, 209

British Museum’s Great Court

, 189

London City Hall

, 110

London “Gherkin,”

, 11

Millennium Tower

, 12

Sainsbury Center for Visual Arts

, 137, 182

Franzen, Ulrich

Dana House

, 18, 202

Fujimoto, Sou

House N

, 50, 51

Serpentine Gallery Pavilion

, 101

Fuller, R. Buckminster

, 9

Full penumbras

core-centered

, 200–207

void-centered

, 207–210

Full radial arrays

, 174–176

void-centered

, 188

Full shell arrays

core-centered

, 189–191

void-centered

, 196–197

Gannett/USA Today headquarters

, 196

Gehry, Frank

Biomuseo

, 153–154

Cabrillo Marine Museum

, 19, 20, 29

California Aerospace Museum

, 29, 30

Guggenheim Museum Bilbao

, 250

Millennium Park Amphitheater

, 101, 123

Walt Disney Concert Hall

, 124–125

Winton guest house

, 25, 27, 202

Getty Center, Los Angeles

, 214, 215

Glass House

, 214

Glass skyscraper project

, 108

Goff, Bruce

Bavinger house

, 117, 254

Goldenberg house

, 252

Gordon Strong Automobile Objective

, 117

Grand Central Station

, 246

Grande Arche de la Défense

, 156, 193, 224

Graves, Michael

Art Department and Museum (project), Vassar College

, 22–23, 176, 177

Hanselmann House

, 167–168, 236–237

Kalko residence

, 77

Portland Building

, 50–52, 109

Schulman house renovation/addition

, 54, 55

Great lawn building complex, University of Virginia

, 238

Great Minaret (Samarra, Iraq)

, 117

Great Mosque of Córdoba

, 179

Greenhouse-house

, 19, 20

Grids

, 245–247

Gropius, Walter

Bauhaus Building

, 158–159, 253

Guggenheim Museum Bilbao

, 250

Gwathmey, Charles

Amagansett parents’ house

, 142–143

Habitat project

, 71

Habitat

, 67, 35, 36

Hadid, Zaha

Eli & Edythe Broad Art Museum

, 109–110

Guangzhou Opera House

, 119–120

Heydar Aliyev Center

, 132–133

Rosenthal Center

, 33–34

Hanselmann House

, 167–168, 236–237

Hardy Holzman Pfeiffer

Cummins Occupational Health Center

, 30, 31

Hardy House

, 211

Harmon, Arthur Loomis

Empire State Building

, 144–145

Harmon, Frank

AIA NC Center for Architecture and Design

, 154

Hartsfield-Jackson Airport

, 158, 159, 181, 242

Harvard University

Carpenter Center for the Visual Arts, Harvard University

, 42–43, 44, 161–162, 242, 243

Gund Hall

, 88–89

J.F.K. School of Government

, 115

Larsen Hall

, 92, 93

Old Harvard Yard

, 207, 208

undergraduate dormitories

, 208, 216–217

Hawksmoor, Nicholas

Christ Church Spitalfields

, 61, 62

St. Alfege

, 61

St. Anne’s Limehouse

, 61, 62

St. Mary Woolnoth

, 61

Haystack Mountain School of Crafts

, 180, 181, 183

Heery & Heery

Tallahassee City Hall

, 104

Heifer International’s Headquarters

, 196

Hejduk, John

Wall House II/Bye house

, 35, 36, 122–123, 168, 222, 236, 237

Helsinki house

, 216

Hercules Headquarters

, 146–147, 191

Herniation

, 263

Herzog & de Meuron

de Young Museum

, 147–148, 256–257

Walker Art Center Expansion

, 28

Heydar Aliyev Center

, 132–133

HHPA

Pingry School

, 116

Hibiscus house

, 52, 53

High Museum, Atlanta

, 45

Hilbersheimer, Ludwig

commercial blocks design

, 186

Hillside Home School

, 15

History Faculty Library, Canbridge

, 235–236

Holl, Steven

Tianjin EcoCity Ecology and Planning Museums

, 95

Hollein, Hans

Städtische Museum Abteiberg (Municipal Museum Abteiburg)

, 21, 22, 212, 213

Hood & Howells

New York Daily News Building

, 97–98

Hood, Raymond

McGraw Hill Building

, 87, 88

RCA Building (GE Building)

, 96–97

Horton Plaza

, 76

Hotel P

, 234

House N

, 50, 51

House X

, 155, 156, 267

Houston’s YWCA Masterson Branch

, 107–108

Howe & Lescaze

PSFS Building

, 145–146

Hydraulic lifts

, 36

Icosahedron

, 8

Implosion

, 150

Implosive deformation

, 125–126

Implosive energy

, 26

Incremental shell arrays

core-centered

, 192–193

void-centered

, 193–197

Incremented radial arrays

core-centered aligned partial penumbras

, 217

core-centered full penumbras

, 200–202

core-centered partial penumbras

, 210–211

void-centered aligned partial penumbras

, 221–222

void-centered full penumbras

, 207–208

void-centered partial penumbras

, 213–215

Inland Steel Building

, 139, 218

Inn at Middleton Place

, 217

Isomorphism

, 46

Isozaki, Arata

Okanoyama Graphic Art Museum

, 47–48, 192–193, 235, 264

Jacobsen, Hugh Newell

Blumenthal house

, 213

Buckwalter House

, 51, 52, 56–58

Dreier-Barton house

, 46, 47

Jacobs house

, 178, 179, 221, 267

Putterman house

, 25, 27, 134–135

Waddell House

, 14

Zamoiski House

, 16, 193, 194

Jaeger beach house

, 28

Jakob + Macfarlane

Orange Cube

, 94

Jeanneret, Pierre

Cité de Refuge

, 135

Jeddah’s Kingdom Tower

, 11

Jefferson, Thomas

great lawn building complex, University of Virginia

, 238

University of Virginia’s great lawn building complex

, 178–179

Jerde, John

Horton Plaza

, 76

J.F.K. School of Government

, 115, 166

Johansen, John

Connecticut private residence

, 206

greenhouse-house

, 19, 20

Mummers Theater

, 17, 19

John F. Kennedy Presidential Library & Museum

, 29

John Hancock Tower

, 110

Johns-Manville Headquarters

, 15–16, 184

Johnson, Herbert

, 176

Johnson, Philip

, 101

Boissonnas House

, 65, 66

Cambridge’s Johnson house

, 157, 158

Erik Boissonnas house II

, 134, 249, 250

Glass House

, 214

Johnson House

, 203, 204

Seagram Building

, 98–99

Jones Laboratory

, 32, 33, 239, 240

Joy, Rick

Desert Nomad House

, 14

Kaaba, Makkah, Saudi Arabia

, 8

Kahn, Louis I.

Bangladesh Assembly Building

, 207

Dhaka Assembly Building

, 23, 25

Dominican Motherhouse

, 160, 161, 229

Erdman Hall Dormitories

, 47, 244, 245

Exeter library

, 189

Goldenberg house

, 123–124, 252

Kimbell Art Museum

, 66

Phillips Exeter Academy Library

, 49, 51, 124, 247, 271

Richards Medical Research Laboratories, University of Pennsylvania

, 249, 250

Salk Institute for Biological Studies

, 42, 106, 107, 187

Kalko residence

, 77

Kallmann, McKinnell and Knowles

Boston City Hall

, 37–38, 39, 208, 209

Kiesler, Frederick

Endless House

, 148, 149

Kimbell Art Museum

, 66

Kittredge dormitories

, 182, 183

KJA

Annie Maxim House

, 115

Klontz & Wrede

Belleview Square

, 175

Koolhaas

, 8

KPF

AT&T Long Lines

, 182

Gannett/USA Today headquarters

, 196

Hercules Headquarters

, 146–147, 191

Proctor & Gamble Headquarters

, 178

Kress residence

, 47

Kunsthaus Graz

, 119

Lake Neuchatel’s Blur Building

, 101

Lamb, William F.

Empire State Building

, 144

Lawrence Residence

, 31

Le Corbusier

Ahmedabad Mill Owners’ Association Building

, 152–153

Carpenter Center for the Visual Arts (Harvard University)

, 42–43, 44, 161–162, 242, 243

Cité de Refuge

, 135

City of Refuge, Paris

, 234

Couvent Sainte Marie de La Tourette

, 165–167, 255–256

Firminy’s Youth & Cultural Center

, 90

Mundaneum

, 117

Notre Dame du Haut

, 125

Palace of Assembly, Chandigarh

, 244, 245

Swiss Pavilion, Paris

, 139, 164–165, 243–244

Villa Savoye

, 36–37, 38, 81–82, 86–87

Ledge House

, 213–214, 215

Ledoux

, 9

Leicester University

Engineering Building

, 62, 84, 138

Leslie Martin & Colin St. John Wilson

Cambridge University’s Harvey Court

, 158

Lever House

, 35, 37

Leverkusen Cultural Center

, 231–232

Leyswood house

, 210

Libeskind, Daniel

Jewish Museum

, 114–115

Library of France

, 8, 91

Ligornetto House

, 222

Lincoln Cathedral

, 163

Linear dimensionalities

, 135–137

Linear duplication

, 47–48

elevational cases

, 48

plan cases

, 48

Linear hybrids

, 158–160

Linear link geometries, sequential tree of

, 18

Linear linking

, 228–229

addition

, 15–17

Linear regression

, 48–55

one dimension regression

, 53–55

two dimensions/direct (2d/direct)

, 49–55

Lister County Courthouse

, 212

Lloyd Lewis House

, 248, 249

Long Gallery House project

, 138, 182

Long Wharf Marriott Hotel

, 86, 89, 137, 179, 180

Los Angeles’ Pacific Design Center

, 90–91

Louisiana Museum

, 16, 236

Lovell House

, 96, 97

Lutyens, Edwin

Thiepval Memorial Arch

, 98

Luzerne County Community College Conference Center

, 138

MacLean, Amsler Hagenah

Wharton house

, 53

Macy’s Headquarters

, 80

Mahlum

Wilkes Elementary School

, 246

Maison Carré

, 90

Mandell Residences

, 221

Manhattan

New Museum

, 34, 35

Paramount Building

, 50, 51

World Financial Center

, 59

Margaret Hotel

, 59–60, 191

Mario Botta

Swiss villas

, 88

Mast Family General Store, North Carolina

, 221

Matrix embedding

, 17–21, 29

McGraw Hill Building

, 87, 88

Meier, Richard

Atheneum Visitor Center

, 168–169

Cornell University Undergraduate Housing

, 137

Douglas House

, 43, 44, 214

Getty Center, Los Angeles

, 214, 215

High Museum, Atlanta

, 45

Museum of Decorative Arts, Frankfurt am Main

, 43, 45, 233

Shamberg House

, 43, 44

Smith house

, 43, 218–219, 220

Mendelsohn, Erich

Einstein Tower

, 118, 119

Mesoamerican civilizations

, 8

Mies van der Rohe, Ludwig

, 157

Barcelona Pavilion

, 149–150

Farnsworth house

, 36, 37, 128, 129

glass skyscraper project

, 108

Seagram Building

, 98–99

Millennium Tower

, 12

Minority Airport Architects

Hartsfield-Jackson Airport

, 158, 159

Mission Park Houses project, Williams College

, 163–164

MIT’s Maclaurin Buildings

, 178, 179

Mitchell/Giurgola

AIA Headquarters

, 80

Lang Music Building

, 42, 43

Mission Park Houses project, Williams College

, 163–164

State University of New York’s Student Center

, 79–80

Tredyffrin Public Library

, 153, 195, 196

MLTW

Sea Ranch Condominium

, 26, 27, 46, 84, 231

Moffett, Marian

, 175

Moore, Charles

, 20, 21, 32, 33

Hines House

, 180

Moore house

, 32, 33, 141, 244, 245

Stern House

, 30, 31

Moore Grover Harper

Jones Laboratory

, 32, 33, 239, 240

Morgan, William

Thomas house

, 92–93

Morphing

, 251–252

core-centered full penumbras

, 206–207

void-centered full penumbras

, 210

Morphosis

Emerson Los Angeles

, 156, 157

Lawrence Residence

, 31

Moscow

road connector network

, 189

Mount Angel Benedictine College

, 121, 122

Mount Zion Seventh-Day Adventist Church

, 60, 61

Multifamily housing

, 26

Multiple floors, slab-sided column of

, 35

Mummers Theater

, 17, 19, 241, 242

Mundaneum

, 117

Murphy, C. F.

Xerox Center

, 81, 82

Murphy/Jahn

State of Illinois Center (James R. Thompson Center)

, 203, 209

Museum for Northrhine Westphalia

, 208–209

Museum of Decorative Arts, Frankfurt am Main

, 43, 45, 233

National Library of France

, 151

Neue Staatsgalerie Stuttgart

, 23, 24, 209, 241–242

Neue Vahr apartments

, 122

Neutra, Richard

Lovell House

, 96, 97

New York

Daily News Building

, 97–98

1939–1940 World’s Fair

, 9

North Dade Justice Center

, 34, 35

Northrhine Westphalia Museum

, 78, 79

Notre Dame du Haut

, 42, 125, 126

Nouvel, Jean

Fondation Cartier

, 129, 194, 195

Tour Sans Fins

, 136

Obelisque

, 193

Obfuscation

, 31

Octagon House

, 80

Okanoyama Graphic Art Museum

, 47–48, 235, 264

Old Harvard Yard, Harvard University

, 207, 208

Old Radcliffe Yard, Radcliffe University

, 207–208, 213

Oliver, Richard

, 20, 21

Olivetti Training School

, 116

OMA

CCTV Headquarters

, 94, 159

Library of France

, 91

Seattle Public Library

, 33, 34

Très Grande Bibiothèque competition entry

, 32–33

Omnidirectional deformation

, 123–125

One dimension (1d) regression

, 53–55

elevational cases

, 53, 54

plan cases

, 54

Onion domes

, 108–109

“Opposites attract” approach

, 43

Orange Cube

, 94

Oscar Hoff

Ullevål Haveby

, 247, 248

Oslo Opera House

, 112–113

Otaniemi Technical University (Aalto University)

, 67, 161

Oud, J. J. P.

Weissenhof Row Houses

, 222, 223

townhouses

, 230

Oxford University

Florey Building

, 162–163, 216

Paatelainen, Raili Inkeri Marjatta

Dipoli student center

, 105

Paimio Sanitorium

, 16–17

Palace Condominium

, 31, 32, 131

Palace Condos

, 131

Palace of Assembly, Chandigarh

, 62, 244, 245

Palacio de Carlos V

, 238, 239

Palacio de Comares

, 238, 239

Palacio del Leones

, 238, 239

Palazzo Spada

, 52

Palladio, Andrea

Vila Capra

, 235

Parc de la Villette

, 67–68, 248

Parthenon

, 258

Parti

, 32

Partial penumbras

aligned

, 217–223

core-centered

, 210–213

void-centered

, 213–217

Partial radial arrays

, 177–178

aligned

, 178–179, 185–187

void-centered

, 187–188

Partial shell arrays

core-centered

, 191

void-centered

, 195–196

Partial single shells

core-centered partial penumbras

, 211–212

void-centered partial penumbras

, 215–217

Pei, I. M.

East Wing, National Gallery, Washington, D.C.

, 205, 235

Everson Museum of Art

, 43, 45, 85, 86, 251, 252

John F. Kennedy Presidential Library & Museum

, 29

Paul Mellon Arts Center, Choate Rosemary Hall School

, 42, 43, 224, 225

Pelli, César

Long Gallery House project

, 138, 182

Los Angeles’ Pacific Design Center

, 90–91

Manhattan’s World Financial Center

, 59

World Financial Center

, 97, 190

Penumbra

, 199

aligned partial

, 217–223

full

, 200–210

partial

, 210–217

unitary redux

, 223–226

Perkins+Will

William Jones College Preparatory High School

, 93–94, 114–115

Perrault, Dominique

Ewha Womans University

, 100

National Library of France

, 151

Peter’s Basilica, Vatican City

, 44, 45

Phillips Exeter Academy Library

, 49, 51, 124, 247

Piano’s London “Shard,”

, 11

Piazza San Marco & Piazzetta

, 245

Piazzi della Cisterna

, 245

Piazzi della Signoria and del Duomo

, 245

Pierre Jeanneret

City of Refuge, Paris

, 234

Pietilä, Reima

Dipoli student center

, 105

Pingry School

, 116, 164, 169

Place de l’Étoile (Place Charles de Gaulle)

, 175, 176

Planar/linear form of dimensionalities

, 139

Planar/linear hybrids

, 162–163

Planar duplication

, 65–68, 246

Planar form of dimensionalities

, 128–133

Planar hybrids

, 149–152

Planar regression

, 68–71

Plan-oriented subtraction

corner-removal types, sequential array of

, 81

edge-centered (one dimension)

, 76–77

edge-centered (two dimension)

, 78–79

face-centered (one dimension)

, 75–76

face-centered (three dimension)

, 81–82

face-centered (two dimension)

, 77–78

types of

, 74

vertex-centered (two dimension)

, 79–81

Plastic

bending

, 113–115

failure

, 115–116

shear deformation

, 109–110

tension

, 104–105

Plasticity

, 105

Plater-Zyberk, Duany

Hibiscus house

, 52, 53

Platonic solids

, 7–8

Poetry Foundation Building

, 229–230

Polshek, James

Rose Center for Earth & Space

, 9, 44–46

Polyhedral basics

, 7–10

Portland Building

, 50–52, 109

Portland Museum of Art

, 52–53

Portman, John

Atlanta Hyatt Regency

, 78

Hyatt

, 89

Postmodernism

, 19

“Powers of Ten,”

, 215

Predock, Antoine

American Heritage Center

, 12

Tang Teaching Museum & Art Gallery, Skidmore College

, 176, 177

Proctor & Gamble Headquarters

, 178

Propylaea

, 258

PSFS Building

, 145–146

Putterman house

, 25, 27, 134–135, 230

Pyramide du Louvre

, 8

Quigley, Rob Wellington

Jaeger beach house

, 28

Radcliffe University

Old Radcliffe Yard

, 207–208, 213

Radial increments

, 229

Radials

core-centered

, 174–181

void-centered

, 181–188

Rapp & Rapp

Manhattan’s Paramount Building

, 50, 51

Ravenna’s Basilica of San Vitale

, 206

RCA Building (GE Building)

, 96–97

Regression

evolution of

, 56, 64

linear

, 48–55

one dimension regression

, 53–55

planar

, 68–71

singular

, 44–47, 203

two dimensions/direct

, 49–55

two dimensions/inverse

, 55–65

volumetric

, 64, 71–72

Reid Building of the Glasgow School of Art

, 143

Replication

, 16, 41–72, 263

cores

, 245

evolution of

, 56, 64

grids

, 245–247

linear duplication

, 47–48

linear regression

, 48–55

one dimension regression

, 53–55

planar duplication

, 65–68

planar regression

, 68–71

singular duplication

, 41–44

singular regression

, 44–47

taxonomy of

, 63

two dimensions/direct

, 49–55, 57–60

two dimensions/inverse regression

, 55–65

volumetric duplication/regression

, 64, 71–72

Richards Medical Research Laboratories, University of Pennsylvania

, 249, 250

Richardson, Henry Hobson

Allegheny County Courthouse

, 77–78

Rietveld, Gerrit

Schröder House

, 129–130

Rigid failure

, 116

Robie house

, 35–36

Robson, Sheppard

Sainsbury Wing of London’s National Gallery

, 107

Roche & Dinkeloo

College Life Insurance Company

, 66, 67

Ford Foundation Building, Manhattan

, 212, 213

Roman Pantheon

, 225

Ronan, John

Poetry Foundation Building

, 229–230

Roof chamfers

, 89–90

Rose Center for Earth & Space

, 9, 49

Rosenbaum house

, 178, 179

Rosenthal Center

, 33–34

Rovaniemi Library

, 121, 122

Rowes Wharf

, 162

RTKL

Cincinnati’s Federated building

, 80, 81, 96

Rudolph, Paul

Yale Art & Architecture Building (Rudolph Hall)

, 150

Rutgers Business School

, 159–160

Saarinen’s Kresge Auditorium

, 9, 10

Sackler Museum

, 113, 180

Safdie, Moshe

Ben Gurion Airport Tel Aviv

, 174–175

Habitat project

, 71

Habitat

, 67, 35, 36

Sainsbury Center for Visual Arts

, 137, 182

Sainsbury Wing of London’s National Gallery

, 107

St. Alfege

, 61

St. Anne’s Limehouse

, 61, 62

St. Mary Woolnoth

, 61

St. Paul’s School’s Kittredge Dormitories

, 160

St. Peter’s Scala Regia

, 52

Salisbury Cathedral

, 31, 32

Salk Institute for Biological Studies

, 187

Säynätsalo Town Hall

, 21, 22

Scarborough College

, 252–253, 259

Schindler, Rudolph

Schindler house

, 253

Schinkel, Karl Friedrich

Altes Museum

, 23, 24

School of Architecture Building, Florida A&M University

, 230–231

Schröder House

, 129–130

Schulman house renovation/addition

, 54, 55

Schwarz, Rudolf

The Church Incarnate: The Sacred Function of Christian Architecture

, 275

Scutt, Der

Trump Tower

, 95–96

Sea Ranch Condominium

, 26, 27, 46, 84, 231

Seattle Public Library

, 33, 34

Seinäjoki Library

, 121, 122

Selfridges Building

, 119

Serpentine Gallery Pavilion

, 101

Shamberg House

, 43, 44

Shaw, Richard Norman

Leyswood house

, 210

Shear deformation

plastic shear

, 109–110

shear failure

, 111–113

Shells

core-centered

, 188–193

sequence of

, 189

void-centered

, 193–197

Shelly Ridge Girl Scout Center’s Activity Lodge

, 76

Shiraz Art Museum

, 113–114, 233–234

Shreve, Richmond

Empire State Building

, 144

Siedlung Westhausen

, 247, 248

Siegel, Gwathmey

, 150–151

Siena’s Palazzo Pubblico

, 137

Single radials

core-centered

, 179–181

void-centered

, 181–185

Single shells

core-centered full penumbras

, 202–204

void-centered full penumbras

, 208–210

Singular duplication

, 41–44, 106

planar

, 43, 44

Singular regression

, 44–47, 203

Skidmore College

Tang Teaching Museum & Art Gallery

, 176, 177

Slipped variant, evolution of

, 96

Smith Hinchman & Grylls Architects

Hartsfield-Jackson Airport

, 158, 159

Smith house

, 43, 218–219, 220

Snøhetta

Bibliotheca Alexandrina

, 10

Oslo Opera House

, 112–113

Soleri, Paolo

“Babel IIB,” hypothetical design

, 71–72

SOM

Cayan Tower

, 118

Inland Steel Building

, 139

Lever House

, 35, 37

Rowes Wharf

, 85, 162

University of Iowa’s Bowen Science Building

, 71

Southern Appalachians, vernacular cantilever barn of

, 240

Spear house

, 195

Staatsgalerie

, 47

Städtische Museum Abteiberg (Municipal Museum Abteiburg)

, 21, 22, 212, 213

State of Illinois Center (James R. Thompson Center)

, 203, 209

State University of New York’s Student Center

, 79–80

Stern House

, 30, 31

Steven Holl & JM Architects

Reid Building of the Glasgow School of Art

, 143

Stevens & Wilkinson Architects

Hartsfield-Jackson Airport

, 158, 159

Stevie Ellis Dance Theater

, 158

Stirling, James

Cambridge History Faculty Building

, 79

Florey Building, Oxford University

, 216

History Faculty Library, Canbridge

, 235–236

Leicester University’s Engineering Building

, 62, 84, 138

Leicester Engineering Building

Museum for Northrhine Westphalia

, 208–209

Neue Staatsgalerie Stuttgart

, 23, 24, 47

Northrhine Westphalia Museum

, 78, 79

Olivetti Training School

, 116

Oxford University’s Florey Building

, 162–163

Palace of Assembly, Chandigarh

, 62

Sackler Museum

, 113, 180

University of St. Andrews’s Andrew Melville Hall

, 138

University of St. Andrews’s dormitories

, 177–178

Wissenschaftszentrum Berlin für Sozialforschung

, 22, 23

Stirling & Wilford

Braun Headquarters

, 139–140

Neue Staatsgalerie Stuttgart

, 241–242

Wissenschaftszentrum Berlin für Sozialforschung

, 207

Stockholm Public Library

, 23, 24, 235

Stubbins, Hugh

Citicorp Center

, 89

Subtraction

, 3, 73–101, 262, 263

elevation-oriented

one dimension

, 82–84

three dimension

, 91–96

two dimension

, 84–91

interventions of

, 74

mediating cases, variants of

, 96–99

plan-oriented

one dimension

, 75–77

three dimension

, 81–82

two dimension

, 77–81

ultimate

, 99–101

Subtractive accommodation

, 249–251

Subtractive incrementation

, 247–248

Superposition

, 130, 234–239

addition

, 30–32, 44

cohesion

, 31

collidive angles, sequence of

, 31

core-centered full penumbras

, 205

obfuscation

, 31

Swiss Pavilion

, 139, 164–165, 243–244

Sydney Opera House

, 151, 187

Taft Architects

Houston’s YWCA Masterson Branch

, 18–19, 107–108

Tallahassee City Hall

, 104

Tang Teaching Museum & Art Gallery, Skidmore College

, 176, 177

TEN Arquitectos

Rutgers Business School

, 159, 160

Tensile deformation

, 104–107, 263

plastic tension

, 104–105

tensile failure

, 105–107

The Architects Collaborative (TAC)

Johns-Manville Headquarters

, 15–16, 184

Thiepval Memorial Arch

, 98

Thomas house

, 92–93

Tod Williams & Billie Tsien

Barnes Foundation

, 147, 256, 257

Tokyo International Forum

, 220

Tomek house

, 218, 220

Torque deformation

, 117–118

Touching

, 21–23, 229–230

Tour Sans Fins

, 10, 12, 136

Tower of Babel

, 117

Toyo Ito

Hotel P

, 234

Transamerica Pyramid

, 10, 11

Tredyffrin Public Library

, 153, 195, 196

Très Grande Bibiothèque competition entry

, 32–33

Troglytism

, 99

Tschumi, Bernard

Parc de la Villette

, 67–68, 248

Turnbull, William

Hines House

, 180

lattice-wrapped house

, 190

Zimmerman House

, 54, 55

Two dimensions/direct (2d/direct) regression

, 49–55

compared with two dimensions/inverse regression

, 57–60

elevational cases

, 49, 50

plan cases

, 49, 50

Two dimensions/inverse regression

, 55–65

compared with two dimensions/direct regression

, 57–60

elevational cases

, 57, 58

plan cases

, 57, 58

Ullevål Haveby

, 247, 248

Ultimate subtraction

, 99–101

Undergraduate dormitories, Harvard University

, 208, 216–217

Underground house design

, 99–100

Unitary form

, 7–12

polyhedral basics

, 7–10

Unitary redux

, 223–226

core-centered

, 225

linking

, 225–226

void-centered

, 223–225

Unity Temple

, 15, 228–229, 247

University of Iowa

Bowen Science Building

, 71

University of Pennsylvania

Richards Medical Research Laboratories

, 249, 250

University of St. Andrews

Andrew Melville Hall

, 138

dormitories

, 177–178

University of Virginia

great lawn building complex

, 178–179, 238

USA county seat town squares

, 175

U.S. Capitol

, 237–238

Usonian houses

, 178, 190

Utzon, Jorn

Sydney Opera House

, 151, 187

Van Alen, William

Chrysler Building

, 144, 145

Vanna Venturi House

, 202

Vassar College

Art Department and Museum (project)

, 22–23, 176, 177

Venturi, Robert

Bermuda house

, 213

Columbus Fire Station

, 138

Fire Station 4, Columbus

, 212

Vanna Venturi House

, 202

Vernacular house porches

, 86, 87

Vertex-centered subtraction

concave mode

, 79–80

convex mode

, 81

elevation-oriented (three dimension)

, 93–96

elevation-oriented (two dimension)

, 86–91

mediating mode

, 80–81, 87, 95

plan-oriented (two dimension)

, 79–81

Viipuri Library

, 111–112, 192, 250–251

Vila Capra

, 235

Villa Chang

, 30, 31

Villa Savoye

, 36–37, 38, 81–82, 86–87

Villa Snellman

, 22, 23

Viñoli, Rafael

Tokyo International Forum

, 220

Void-centered aligned partial penumbras

, 221–223

aligned incremented radial arrays

, 221–222

aligned single shells

, 222

linking

, 223

sequence of

, 221

Void-centered full penumbras

, 207–210

on hub or center

, 209, 210

incremented radial arrays

, 207–208

linking

, 210

sequence of

, 207

single shells

, 208–210

Void-centered partial penumbras

incremented radial arrays

, 213–215

linking

, 217

partial single shells

, 215–217

sequence of

, 214

Void-centered radials

, 181–188

aligned partial radial arrays

, 185–187

full radial arrays

, 188

partial radial arrays

, 187–188

sequence of

, 181

single radials

, 181–185

Void-centered shells

, 193–197

aligned partial shell arrays

, 194–195

full shell arrays

, 196–197

incremental shell arrays

, 193–194

partial shell arrays

, 195–196

sequence of

, 194

Volume-centered suspension (elevation-oriented, three dimension)

, 91–92

Void-centered unitary redux

, 223–225

Volumetric/linear form of dimensionalities

, 137–138

Volumetric/linear hybrids

, 160–162

Volumetric/planar/linear form of dimensionalities

, 139–140

Volumetric/planar/linear hybrids

, 163–170

Volumetric/planar form of dimensionalities

, 133–135

vernacular houseform

, 133

Volumetric/planar hybrids

, 152–157

Volumetric hybrids

, 142–148

von Sprekelsen, Johann Otto

Grande Arche de la Défense

, 85, 224

VSRB

Brant House

, 104

Sainsbury Wing of London’s National Gallery

, 107

Waddell House

, 14

Walker Art Center Expansion

, 28

Wall House II/Bye house

, 35, 36, 122–123, 168, 236, 237

Ward Willits House

, 134

Warping stress deformation

, 113–114

Wells, Malcolm

underground house design

, 99–100

Wexner Center

, 182–183

Wharton house

, 53

Whitney Museum of American Art

, 87–88

Wilford, Michael

Neue Staatsgalerie Stuttgart

, 23, 24

Wissenschaftszentrum Berlin für Sozialforschung

, 22, 23

Wilkes Elementary School

, 246

William Jones College Preparatory High School

, 93–94

Williams College

, 166, 169

Mission Park Houses project

, 163–164

Wingspread

, 176

Winton guest house

, 25, 27, 202

Wissenschaftszentrum Berlin für Sozialforschung

, 22, 23, 207

Wolfsburg Cultural Center

, 52, 113

World Financial Center

, 267

Wright, Frank Lloyd

Barton house

, 32

Cheney house

, 203–204

David & Gladys Wright House

, 117, 118

Edwin Cheney house

, 190

Fallingwater

, 59–61, 214, 254, 255

Gordon Strong Automobile Objective

, 117, 254

Hardy House

, 211

Jacobs house

, 178, 179

Lloyd Lewis House

, 248, 249

Pew House

, 57, 58

Robie house

, 35–36, 111

Rosenbaum house

, 178, 179

Tomek house

, 218, 220, 243

Unity Temple

, 15, 228–229, 247

Ward Willits House

, 134

Wingspread

, 176

Yahara Boat House

, 30

Xerox Center

, 81, 82

Yahara Boat House

, 30

Yale Art & Architecture Building (Rudolph Hall)

, 150

YWCA

, 18–19, 107–108

Zamoiski House

, 16, 193, 194

“Z axis” cases

, 185, 236, 240–244

addition

, 29, 33–39

reversal of additive sequence

, 33, 34

Zimmerman House

, 54, 55