Designation

Name

Short Name

Bases

K4.1

Pentachoron

Pen

Point

Tetrahedron

Dyad

Perpendicular triangle

K4.2

Hexadecachoron

Hex

Tetrahedron

Dual tetrahedron

K4.3

Octahedral pyramid

Octpy

Point

Octahedron

Triangle

Gyro Tetrahedron

K4.4

Square scalene

Squasc

Point

Square pyramid

Dyad

Tetrahedron

Triangle

Inclined triangle

Dyad

Perpendicular square

K4.5

Rectified pentachoron

Rap

Tetrahedron

Octahedron

K4.6

Triangular antifastegium

Traf

Tetrahedron

Square pyramid

Triangle

Octahedron

Triangle

Gyro triangular prism

K4.7

Triangular prismatic pyramid

Trippy

Dyad

Square pyramid

Triangle

Tetrahedron

Point

Triangular prism

Triangle

Ortho square

K4.8

Bidiminished rectified pentachoron

Bidrap

Triangle

Square pyramid

Square

Tetrahedron

Dyad

Ortho triangular prism

K4.9

Tetrahedral prism

Tepe

Tetrahedron

Tetrahedron

Dyad

Para triangular prism

Square

Ortho square

K4.10

Triangular duoprism

Triddip

Triangle

Triangular prism

K4.11

Octahedral prism

Ope

Octahedron

Octahedron

Triangular prism

Gyro triangular prism

K4.12

Square pyramidal prism

Squippyp

Square pyramid

Square pyramid

Square

Triangular prism

Dyad

Cube

K4.13

Dyadic gyrotegmipucofastegium

Dygytpuf

Triangular prism

Reflected ortho triangular prism

K4.14

Square antifastegium

Squaf

Square

Square antiprism

Square

Gyro cube

K4.15

Octahedron atop cube

Octacube

Octahedron

Cube

K4.16

???

???

Square pyramid

Gyro cube

K4.17

Square antiprismatic pyramid

Squappy

Square

Gyro square pyramid

Point

Square antiprism

K4.18

Triangularsquare duoprism

Tisdip

Triangular prism

Triangular prism

Square

Cube

K4.19

Square antiprismatic prism

Squappip

Square antiprism

Square antiprism

Cube

Gyro Cube

K4.20

Tesseract

Tes

Cube

Cube

K4.21

Cube atop icosahedron

Cubaike

Cube

Icosahedron

K4.22

Pentagonal antifastegium

Paf

Pentagon

Pentagonal antiprism

Pentagon

Gyro pentagonal prism

K4.23

Tetrahedron atop cuboctahedron

Tetaco

Tetrahedron

Cuboctahedron

K4.24

Tetrahedron atop triangular cupola

Tetatricu

Tetrahedron

Triangular cupola

K4.25

Triangular cupofastegium

Tricuf

Triangle

Triangular cupola

Hexagon

Triangular prism

K4.26

Cubic pyramid

Cubpy

Square

Square pyramid

Point

Cube

K4.27

Triangular antiwedge

Traw

Triangle

Gyro triangular cupola

Hexagon

Octahedron

K4.28

Bidiminished octahedron atop cuboctahedron

Bidoctaco

Square

Cuboctahedron

K4.29

Octahedron atop cuboctahedron

Octaco

Octahedron

Cuboctahedron

K4.30

Octahedron atop triangular cupola

Octatricu

Octahedron

Triangular cupola

K4.31

Square pyramid atop cuboctahedron

Squippiaco

Square pyramid

Cuboctahedron

K4.32

Square pyramid atop triangular cupola

Squippiatricu

Square pyramid

Triangular cupola

K4.33

???

???

Triangle

Tridiminished icosahedron

K4.34

Triangularpentagonal duoprism

Trapedip

Pentagon

Pentagonal prism

K4.35

Cube atop cuboctahedron

Cubaco

Cube

Cuboctahedron

K4.36

Icosahedral prism

Ipe

Icosahedron

Icosahedron

K4.37

Gyroelongated pentagonal pyramidal prism

Gyepippip

Gyroelongated pentagonal pyramid

Gyroelongated pentagonal pyramid

K4.38

Pentagonal pyramidal prism

Peppyp

Pentagonal pyramid

Pentagonal pyramid

Dyad

Pentagonal prism

K4.39

Pentagonal antiprismatic prism

Pappip

Pentagonal antiprism

Pentagonal antiprism

Pentagonal prism

Gyro pentagonal prism

K4.40

Metabidiminished icosahedral prism

Mibdip

Metabidiminished icosahedron

Metabidiminished icosahedron

K4.41

Tridiminished icosahedral prism

Teddipe

Tridiminished icosahedron

Tridiminished icosahedron

K4.42

Squarepentagonal duoprism

Squipdip

Pentagonal prism

Pentagonal prism

K4.43

Cuboctahedral prism

Cope

Cuboctahedron

Cuboctahedron

K4.44

Triangular orthobicupolic prism

Tobcupe

Triangular orthobicupola

Triangular orthobicupola

K4.45

Triangular cupolic prism

Tricupe

Triangular cupola

Triangular cupola

Triangular prism

Hexagonal prism

K4.46

Hexagonal antifastegium

Haf

Hexagon

Hexagonal antiprism

Hexagon

Gyro hexagonal prism

K4.47

Triangularhexagonal duoprism

Thiddip

Hexagon

Hexagonal prism

K4.48

Cuboctahedron atop truncated tetrahedron

Coatut

Cuboctahedron

Truncated tetrahedron

K4.49

Triangular orthobicupola atop truncated tetrahedron

Tobcuatut

Triangular orthobicupola

Truncated tetrahedron

K4.50

Triangular cupola atop truncated tetrahedron

Tricuatut

Triangular cupola

Truncated tetrahedron

K4.51

Triangular pucofastegium

Tripuf

Hexagon

Triangular cupola

Triangle

Hexagonal prism

K4.52

Octahedron atop truncated tetrahedron

Octatut

Octahedron

Truncated tetrahedron

K4.53

Hexagonal antiprismatic prism

Happip

Hexagonal antiprism

Hexagonal antiprism

Hexagonal prism

Gyro hexagonal prism

K4.54

Squarehexagonal duoprism

Shiddip

Hexagonal prism

Hexagonal prism

K4.55

Truncated tetrahedral cupoliprism

Tutcup

Truncated tetrahedron

Inverted truncated tetrahedron

K4.56

Tetrahedron atop truncated tetrahedron

Tetatut

Tetrahedron

Truncated tetrahedron

K4.57

Truncated tetrahedral prism

Tuttip

Truncated tetrahedron

Truncated tetrahedron

K4.58

Octagonal antifastegium

Oaf

Octagon

Octagonal antiprism

Octagon

Gyro octagonal prism

K4.59

Triangularoctagonal duoprism

Todip

Octagon

Octagonal prism

K4.60

Snub cubic prism

Sniccup

Snub cube

Snub cube

K4.61

Cuboctahedron atop small rhombicuboctahedron

Coasirco

Cuboctahedron

Small rhombicuboctahedron

K4.62

Cuboctahedron atop elongated square cupola

Coaescu

Cuboctahedron

Elongated square cupola

K4.63

Cuboctahedron atop octagonal prism

Coaop

Cuboctahedron

Octagonal prism

K4.64

Square antiwedge

Squaw

Square

Gyro square cupola

Octagon

Square antiprism

K4.65

Octagonal antiprismatic prism

Oappip

Octagonal antiprism

Octagonal antiprism

Octagonal prism

Gyro octagonal prism

K4.66

Small rhombicuboctahedral prism

Sircope

Small rhombicuboctahedron

Small rhombicuboctahedron

K4.67

Elongated square gyrobicupolic prism

Esquigybcupe

Elongated square gyrobicupola

Elongated square gyrobicupola

K4.68

Elongated square cupolic prism

Escupe

Elongated square cupola

Elongated square cupola

K4.69

Square cupolic prism

Squacupe

Square cupola

Square cupola

Cube

Octagonal prism

K4.70

Squareoctagonal duoprism

Sodip

Octagonal prism

Octagonal prism

K4.71

Cube atop small rhombicuboctahedron

Cubasirco

Cube

Small rhombicuboctahedron

K4.72

???

???

Cube

Elongated square cupola

K4.73

Square cupofastegium

Squicuf

Square

Ortho square cupola

Octagon

Cube

K4.74

Dodecahedral prism

Dope

Dodecahedron

Dodecahedron

K4.75

Small rhombicuboctahedron atop truncated octahedron

Sircoatoe

Small rhombicuboctahedron

Truncated octahedron

K4.76

Truncated tetrahedron atop truncated octahedron

Tutatoe

Truncated tetrahedron

Truncated octahedron

K4.77

Dodecahedron atop icosidodecahedron

Doaid

Dodecahedron

Icosidodecahedron

K4.78

Icosahedron atop dodecahedron

Ikadoe

Icosahedron

Dodecahedron

K4.79

???

???

Gyroelongated pentagonal pyramid

Dodecahedron

K4.80

Pentagonal antiprismatic pyramid

Pappy

Pentagon

Gyro pentagonal pyramid

Point

Pentagonal antiprism

K4.81

Pentagonal antiprism atop dodecahedron

Papadoe

Pentagonal antiprism

Dodecahedron

K4.82

Metabidiminished icosahedron atop dodecahedron

Mibdiadoe

Metabidiminished icosahedron

Dodecahedron

K4.83

Tridiminished icosahedron atop dodecahedron

Teddi adoe

Tridiminished icosahedron

Dodecahedron

K4.84

Icosahedral pyramid

Ikepy

Point

Icosahedron

K4.85

Gyroelongated pentagonal pyramidal pyramid

Gyepippy

Point

Gyroelongated pentagonal pyramid

K4.86

Pentagonal scalene

Pesc

Point

Pentagonal pyramid

Dyad

Perpendicular pentagon

K4.87

Metabidiminished icosahedral pyramid

Mibdipy

Point

Metabidiminished icosahedron

K4.88

Tridiminished icosahedral pyramid

Teddipy

Point

Tridiminished icosahedron

K4.89

Truncated octahedral prism

Tope

Truncated octahedron

Truncated octahedron

K4.90

Icosidodecahedral prism

Iddip

Icosidodecahedron

Icosidodecahedron

K4.91

Pentagonal orthobirotundic prism

Pobrope

Pentagonal orthobirotunda

Pentagonal orthobirotunda

K4.92

Pentagonal rotundic prism

Perope

Pentagonal rotunda

Pentagonal rotunda

K4.93

Decagonal antifastegium

Daf

Decagon

Decagonal antiprism

Decagon

Gyro decagonal prism

K4.94

Triangulardecagonal duoprism

Tradedip

Decagon

Decagonal prism

K4.95

Cuboctahedron atop truncated octahedron

Coatoe

Cuboctahedron

Truncated octahedron

K4.96

Decagonal antiprismatic prism

Dappip

Decagonal antiprism

Decagonal antiprism

Decagonal prism

Gyro decagonal prism

K4.97

Squaredecagonal duoprism

Squadedip

Decagonal prism

Decagonal prism

K4.98

Truncated octahedron atop truncated cube

Toatic

Truncated octahedron

Truncated cube

K4.99

Truncated cubic prism

Ticcup

Truncated cube

Truncated cube

K4.100

Small rhombicuboctahedron atop truncated cube

Sircoatic

Small rhombicuboctahedron

Truncated cube

K4.101

???

???

Elongated square gyrobicupola

Truncated cube

K4.102

Small rhombicuboctahedron atop gyro truncated cube

Sircoagytic

Small rhombicuboctahedron

Gyro truncated cube

K4.103

???

???

Elongated square cupola

Truncated cube

K4.104

???

???

Elongated square cupola

Gyro truncated cube

K4.105

Square pucofastegium

Squipuf

Octagon

Square cupola

Square

Octagonal prism

K4.106

???

???

Octagonal prism

Truncated cube

K4.107

Octahedron atop small rhombicuboctahedron

Octasirco

Octahedron

Small rhombicuboctahedron

K4.108

???

???

Square pyramid

Elongated square cupola

K4.109

Square pyramid atop square cupola

Squippia squacu

Square pyramid

Square cupola

K4.110

Snub dodecahedral prism

Sniddip

Snub dodecahedron

Snub dodecahedron

K4.111

Small rhombicosidodecahedral prism

Sriddip

Small rhombicosidodecahedron

Small rhombicosidodecahedron

K4.112

Gyrate rhombicosidodecahedral prism

Gyriddip

Gyrate rhombicosidodecahedron

Gyrate rhombicosidodecahedron

K4.113

Parabigyrate rhombicosidodecahedral prism

Pabgyriddip

Metabigyrate rhombicosidodecahedron

Metabigyrate rhombicosidodecahedron

K4.114

Metabigyrate rhombicosidodecahedral prism

Mabgyriddip

Metabigyrate rhombicosidodecahedron

Metabigyrate rhombicosidodecahedron

K4.115

Trigyrate rhombicosidodecahedral prism

Tagyriddip

Trigyrate rhombicosidodecahedron

Trigyrate rhombicosidodecahedron

K4.116

Diminished rhombicosidodecahedral prism

Diriddip

Diminished rhombicosidodecahedron

Diminished rhombicosidodecahedron

K4.117

Pentagonal cupolic prism

Pecupe

Pentagonal cupola

Pentagonal cupola

Pentagonal prism

Decagonal prism

K4.118

Paragyrate diminished rhombicosidodecahedral prism

Pagydriddip

Paragyrate diminished rhombicosidodecahedron

Paragyrate diminished rhombicosidodecahedron

K4.119

Metagyrate diminished rhombicosidodecahedral prism

Magydriddip

Metagyrate diminished rhombicosidodecahedron

Metagyrate diminished rhombicosidodecahedron

K4.120

Bigyrate diminished rhombicosidodecahedral prism

Bagydriddip

Bigyrate diminished rhombicosidodecahedron

Bigyrate diminished rhombicosidodecahedron

K4.121

Parabidiminished rhombicosidodecahedral prism

Pabidriddip

Parabidiminished rhombicosidodecahedron

Parabidiminished rhombicosidodecahedron

K4.122

Metabidiminished rhombicosidodecahedral prism

Mabidriddip

Metabidiminished rhombicosidodecahedron

Metabidiminished rhombicosidodecahedron

K4.123

Gyrate bidiminished rhombicosidodecahedral prism

Gybadriddip

Gyrate bidiminished rhombicosidodecahedron

Gyrate bidiminished rhombicosidodecahedron

K4.124

Tridiminished rhombicosidodecahedral prism

Tedriddip

Tridiminished rhombicosidodecahedron

Tridiminished rhombicosidodecahedron

K4.125

Great rhombicuboctahedral prism

Gircope

Great rhombicuboctahedron

Great rhombicuboctahedron

K4.126

Small rhombicosidodecahedron atop truncated icosahedron

Sridati

Small rhombicosidodecahedron

Truncated icosahedron

K4.127

Truncated icosahedral prism

Tipe

Truncated icosahedron

Truncated icosahedron

K4.128

Truncated cube atop great rhombicuboctahedron

Ticagirco

Truncated cube

Great rhombicuboctahedron

K4.129

Cuboctahedron atop truncated cube

Coatic

Cuboctahedron

Truncated cube

K4.130

Truncated dodecahedral prism

Tiddip

Truncated dodecahedron

Truncated dodecahedron

K4.131

Icosidodecahedron atop small rhombicosidodecahedron

Idasrid

Icosidodecahedron

Small rhombicosidodecahedron

K4.132

???

???

Icosidodecahedron

Diminished rhombicosidodecahedron

K4.133

Pentagonal antiwedge

Paw

Pentagon

Gyro pentagonal cupola

Decagon

Pentagonal antiprism

K4.134

???

???

Icosidodecahedron

Parabidiminished rhombicosidodecahedron

K4.135

???

???

Icosidodecahedron

Metabidiminished rhombicosidodecahedron

K4.136

???

???

Icosidodecahedron

Tridiminished rhombicosidodecahedron

K4.137

Icosahedron atop icosidodecahedron

Ikaid

Icosahedron

Icosidodecahedron

K4.138

???

???

Gyroelongated pentagonal pyramid

Icosidodecahedron

K4.139

Pentagonal pyramid atop pentagonal rotunda

Peppia pero

Pentagonal pyramid

Pentagonal rotunda

K4.140

Gyroelongated pentagonal pyramid atop pentagonal rotunda

Gyepipa pero

Pentagonal pyramid

Pentagonal rotunda

K4.141

Pentagonal prismatic pyramid

Pippy

Pentagon

Pentagonal pyramid

Point

Pentagonal prism

K4.142

Pentagonal antiprism atop icosidodecahedron

Papaid

Pentagonal antiprism

Icosidodecahedron

K4.143

???

???

Metabidiminished icosahedron

Icosidodecahedron

K4.144

???

???

Pentagonal antiprism

Pentagonal rotunda

K4.145

???

???

Metabidiminished icosahedron

Pentagonal rotunda

K4.146

???

???

Pentagon

Pentagonal rotunda

K4.147

Tridiminished icosahedron atop icosidodecahedron

Teddi aid

Tridiminished icosahedron

Icosidodecahedron

K4.148

???

???

Tridiminished icosahedron

Pentagonal rotunda

K4.149

Truncated octahedron atop great rhombicuboctahedron

Toagirco

Truncated octahedron

Great rhombicuboctahedron

K4.150

Great rhombicosidodecahedral prism

Griddip

Great rhombicosidodecahedron

Great rhombicosidodecahedron

K4.151

Truncated icosahedron atop truncated dodecahedron

Tiatid

Truncated icosahedron

Truncated dodecahedron

K4.152

Dodecahedron atop small rhombicosidodecahedron

Doasrid

Dodecahedron

Small rhombicosidodecahedron

K4.153

???

???

Dodecahedron

Diminished rhombicosidodecahedron

K4.154

Pentagonal cupofastegium

Pecuf

Pentagon

Pentagonal cupola

Decagon

Pentagonal prism

K4.155

???

???

Dodecahedron

Parabidiminished rhombicosidodecahedron

K4.156

???

???

Dodecahedron

Metabidiminished rhombicosidodecahedron

K4.157

???

???

Dodecahedron

Tridiminished rhombicosidodecahedron

K4.158

Icosidodecahedron atop truncated icosahedron

Idati

Icosidodecahedron

Truncated icosahedron

K4.159

Small rhombicosidodecahedron atop truncated dodecahedron

Sridatid

Small rhombicosidodecahedron

Truncated dodecahedron

K4.160

???

???

Gyrate rhombicosidodecahedron

Truncated dodecahedron

K4.161

???

???

Parabigyrate rhombicosidodecahedron

Truncated dodecahedron

K4.162

???

???

Metabigyrate rhombicosidodecahedron

Truncated dodecahedron

K4.163

???

???

Trigyrate rhombicosidodecahedron

Truncated dodecahedron

K4.164

???

???

Diminished rhombicosidodecahedron

Truncated dodecahedron

K4.165

Pentagonal pucofastegium

Pepuf

Decagon

Pentagonal cupola

Pentagon

Decagonal prism

K4.166

???

???

Paragyrate diminished rhombicosidodecahedron

Truncated dodecahedron

K4.167

???

???

Metagyrate diminished rhombicosidodecahedron

Truncated dodecahedron

K4.168

???

???

Bigyrate diminished rhombicosidodecahedron

Truncated dodecahedron

K4.169

???

???

Parabidiminished rhombicosidodecahedron

Truncated dodecahedron

K4.170

???

???

Metabidiminished rhombicosidodecahedron

Truncated dodecahedron

K4.171

???

???

Gyrate bidiminished rhombicosidodecahedron

Truncated dodecahedron

K4.172

???

???

Tridiminished rhombicosidodecahedron

Truncated dodecahedron

K4.173

Truncated dodecahedron atop great rhombicosidodecahedron

Tidagrid

Truncated dodecahedron

Great rhombicosidodecahedron
