List of convex segmentochora

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A segmentochoron is a four-dimensional segmentotope, an orbiform polychoron joining two polyhedra (or lower polytopes) in parallel hyperplanes. Klitzing enumerated the convex cases, finding 173 as well as four infinite families[1]

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

Infinite families[edit | edit source]

designation name bases
K4.174 n-gonal antifastegium n-gon n-gonal antiprism
n-gon gyro n-gonal prism
K4.175 triangular n-gonal duoprism n-gon n-gonal prism
K4.176 n-gonal antiprismatic prism n-gonal antiprism n-gonal antiprism
n-gonal prism gyro n-gonal prism
K4.177 square n-gonal duoprism n-gonal prism n-gonal prism

References[edit | edit source]

  1. Klitzing, Richard. [1]