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
|
Triangular-square 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
|
Triangular-pentagonal 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
|
Square-pentagonal 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
|
Triangular-hexagonal 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
|
Square-hexagonal 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
|
Triangular-octagonal 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
|
Square-octagonal 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
|
Triangular-decagonal 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
|
Square-decagonal 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
|