Segmentotope (EntityClass, 11)
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*Dichoral angle between square pyramid and cube: 45° (exact) | *Dichoral angle between square pyramid and cube: 45° (exact) | ||
+ | *Dichoral angle between adjacent square pyramids: 180° - acos(1/3) ≈ 109.4712206345° | ||
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Revision as of 19:34, 27 March 2014
A segmentotope is an orbiform polytope whose vertices lie on two parallel hyperplanes and whose edge lengths are all equal. The set of all convex segmentotopes up to and including 4D has been enumerated by Dr. Richard Klitzing. There are 177 four-dimensional segmentotopes, including some polychora from other categories (such as cube || cube, which is the same as the tesseract). The full list can be obtained from Klitzing's paper (PDF format).
Nomenclature
A segmentotope is denoted by the notation A || B, where A and B are lower-dimensional polytopes. For segmentochora, A and B are usually polyhedra, although one of them can be lower-dimensional, as is the case with the wedges and pyramids.
Some segmentotopes may have multiple designations, for example, (triangular_prism || hexagonal_prism) is the same as (triangular_cupola || triangular_cupola). Where multiple names are possible, the name listed by Klitzing takes precedence.
Properties
Below are some useful properties of selected segmentochora. Klitzing's numbering is written as "K 4.n", as given in his PhD dissertation. Measurements are given in terms of E, the edge length.
# | Name(s) | Cells | Values |
---|---|---|---|
K 4.7 |
|
| |
K 4.26 |
|
|
|
K 4.45 |
triangular_cupola || triangular_cupola |
| |
K 4.51 |
| ||
K 4.69 |
square_cupola || square_cupola |
| |
K 4.105 |
| ||
K 4.117 |
pentagonal_cupola || pentagonal_cupola |
| |
K 4.141 |
| ||
K 4.165 |
|
Classification
Keiji has begun a project to classify all of Klitzing's segmentochora, so that more interesting ones stand out to help future research.
The current classification is as follows, where each number is a K 4.X index:
- 3 regular polychora
- 1, 2, 20
- the 3-pyrotomochoron, a uniform polychoron
- 5
- 21 members of infinite families
- 6, 10, 14, 18, 19, 22, 34, 39, 42, 46, 47, 53, 54, 58, 59, 65, 70, 93, 94, 96, 97
- 4 infinite families (not individual polychora)
- 174, 175, 176, 177
- all 17 prisms of the uniform polyhedra (not 18, because the cube prism is the K 4.20, already counted above)
- 9, 11, 36, 43, 57, 60, 66, 74, 89, 90, 99, 110, 111, 125, 127, 130, 150
- 12 pyramids of CRF polyhedra
- 3, 4, 7, 17, 26, 80, 84, 85, 86, 87, 88, 141
- 25 prisms of orbiform Johnson solids
- 12, 37, 38, 40, 41, 44, 45, 67, 68, 69, 91, 92, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124
- 30 cupolic forms
- 15, 21, 23, 29, 35, 48, 52, 55, 56, 61, 71, 75, 76, 77, 78, 95, 98, 100, 107, 126, 128, 129, 131, 137, 149, 151, 152, 158, 159, 173
- all 10 bicupolic rings (excluding the prisms of the tetrahedron and square pyramid, already counted above)
- 8, 25, 27, 51, 64, 73, 105, 133, 154, 165
- 3 fragments of cupolic forms (excluding the bicupolic rings)
- 109, 139, 146
- the gyrated octahedral prism
- 13
- the trigonal tridiminished-icosahedral wedge
- 33
- 49 gyrations and diminishes of the cupolic forms
- 16, 24, 28, 30, 31, 32, 49, 50, 62, 63, 72, 79, 81, 82, 83, 101, 102, 103, 104, 106, 108, 132, 134, 135, 136, 138, 140, 142, 143, 144, 145, 147, 148, 153, 155, 156, 157, 160, 161, 162, 163, 164, 166, 167, 168, 169, 170, 171, 172
Full list of segmentochora
# | Name | Symbol | Cells | Comments |
---|---|---|---|---|
1 | pyrochoron | x3o3o3o | 5x tetrahedron | |
2 | aerochoron | x3o3o4o | 16x tetrahedron | |
3 | octahedral pyramid | xo3oo4oo | 8x tetrahedron + 1x octahedron | half of aerochoron |
4 | square dipyramid | xo4oo2ox | 4x tetrahedron + 2x square pyramid | quarter of aerochoron |
5 | 3-pyrotomochoron | o3x3o3o | 5x tetrahedron + 5x octahedron | tetrahedral semicupola |
6 | K4.6 | xox3oxo&#x | 3x tetrahedron + 2x octahedron + 3x square pyramid + 1x trigonal prism | |
7 | triangular prism pyramid | xo3oo2xo | 2x tetrahedron + 3x square pyramid + 1x trigonal prism | |
8 | digonal gyrobicupolic ring | xxo2xox&#x | 1x tetrahedron + 4x square pyramid + 2x trigonal prism | bidiminished 3-pyrotomochoron |
9 | tetrahedral prism | x3o3o2x | 2x tetrahedron + 4x trigonal prism | |
10 | duotrianglinder | x3o2x3o | 6x trigonal prism | |
11 | octahedral prism | x3o4o2x | 2x octahedron + 8x trigonal prism | |
12 | square pyramid prism | xx2oo4xo | 2x square pyramid + 4x trigonal prism + 1x cube | |
13 | gyrated octahedral prism | ?? | 4x square pyramid + (4+4)x trigonal prism | |
14 | K4.14 | xox4oxo&#x | 4x tetrahedron + 4x square pyramid + 2x square antiprism + 1x cube | |
15 | staurohedral antiprism | xo4oo3ox | (8+12)x tetrahedron + 1x octahedron + 6x square pyramid + 1x cube | |
16 | K4.16 | ?? | (4+4+4)x tetrahedron + (1+1+4)x square pyramid + 1x square antiprism + 1x cube | |
17 | square antiprism pyramid | oxo4oox&#x | 8x tetrahedron + 2x square pyramid + 1x square antiprism | |
18 | triangular diprism | x3o2x4o | 4x trigonal prism + 3x cube | |
19 | square antiprism prism | ?? | 8x trigonal prism + 2x square antiprism + 2x cube | |
20 | geochoron | x4o3o3o | 8x cube | |
21 | snubdis antiprism | xo4os3os | 8x tetrahedron + 12x square pyramid + 6x trigonal prism + 1x cube + 1x icosahedron | snubdis antiprism |
22 | K4.22 | xox5oxo&#x | 5x tetrahedron + 5x square pyramid + 2x pentagonal antiprism + 1x pentagonal prism | |
23 | tetrahedral pericupola | xx3oo3ox | (1+4)x tetrahedron + (4+6)x trigonal prism + 1x cuboctahedron | |
24 | K4.24 | ?? | 2x tetrahedron + 6x trigonal prism + 2x trigonal cupola | |
25 | triangular orthobicupolic ring | xx3xo2ox | 3x tetrahedron + (1+3)x trigonal prism + 2x trigonal cupola | |
26 | cubic pyramid | xo4oo3oo | 6x square pyramid + 1x cube | |
27 | triangular gyrobicupolic ring | xxo3xox&#x | 1x octahedron + 6x square pyramid + 2x trigonal cupola | |
28 | K4.28 | ?? | (4+8)x square pyramid + 2x cube + 1x cuboctahedron | |
29 | octahedral semicupola | xo3ox4oo | (1+8)x octahedron + 6x square pyramid + 1x cuboctahedron | |
30 | K4.30 | ?? | (2+3)x octahedron + 6x square pyramid + 2x trigonal cupola | |
31 | K4.31 | ?? | 4x octahedron + (1+1+4+4)x square pyramid + 1x cube + 1x cuboctahedron | |
32 | K4.32 | ?? | 1x octahedron + (2+2+4)x square pyramid + 1x cube + 2x trigonal cupola | |
33 | K4.33 | ?? | 3x tetrahedron + 1x octahedron + 3x square pyramid + 1x trigonal prism + 3x pentagonal pyramid + 1x tridiminished icosahedron | trigonal tridiminished-icosahedral wedge |
34 | 5,3-duoprism | x5o2x3o | 5x trigonal prism + 3x pentagonal prism | |
35 | cubic semicupola | xo4ox3oo | 8x tetrahedron + 6x square antiprism + 1x cube + 1x cuboctahedron | |
36 | icosahedral prism | x3o5o2x | 20x trigonal prism + 2x icosahedron | |
37 | gyroelongated pentagonal pyramid prism | ?? | (5+5+5)x trigonal prism + 1x pentagonal prism + 2x gyroelongated pentagonal pyramid | |
38 | pentagonal pyramid prism | xx2oo5xo | 5x trigonal prism + 2x pentagonal pyramid + 1x pentagonal prism | |
39 | pentagonal antiprism prism | ?? | 10x trigonal prism + 2x pentagonal antiprism + 2x pentagonal prism | |
40 | metabidiminished icosahedron prism | ?? | (2+2+2+4)x trigonal prism + 2x pentagonal prism + 2x metabidiminished icosahedron | |
41 | tridiminished icosahedron prism | xxx2xfo3oox | (1+1+3)x trigonal prism + 3x pentagonal prism + 2x tridiminished icosahedron | |
42 | pentagonal diprism | x5o2x4o | 5x cube + 4x pentagonal prism | |
43 | cuboctahedron prism | o4x3o2x | 8x trigonal prism + 6x cube + 2x cuboctahedron | |
44 | trigonal orthobicupola prism | xxx3oxo2xxx | (2+6)x trigonal prism + 6x cube + 2x trigonal orthobicupola | |
45 | trigonal cupola prism | xx3xo2xx | (1+3)x trigonal prism + 3x cube + 2x trigonal cupola + 1x hexagonal prism | half of cuboctahedron prism |
46 | K4.46 | xox6oxo&#x | 6x tetrahedron + 6x square pyramid + 2x hexagonal antiprism + 1x hexagonal prism | |
47 | 6,3-duoprism | x6o2x3o | 6x trigonal prism + 3x hexagonal prism | |
48 | tetrahedral semipericupola | xx3xo3ox | 4x octahedron + 6x trigonal prism + 1x cuboctahedron + 4x trigonal cupola + 1x truncated tetrahedron | |
49 | K4.49 | ?? | 1x octahedron + (3+3)x square pyramid + (3+3)x trigonal prism + 1x trigonal orthobicupola + (1+3)x trigonal cupola + 1x truncated tetrahedron | |
50 | K4.50 | ?? | 1x octahedron + 3x square pyramid + 3x trigonal prism + (1+3)x trigonal cupola + 1x hexagonal prism + 1x truncated tetrahedron | |
51 | triangular magnabicupolic ring | xx3xo2xo | 3x square pyramid + 3x trigonal prism + 2x trigonal cupola + 1x hexagonal prism | |
52 | tetrahedral semimesocupola | xo3xx3oo | 1x octahedron + 4x trigonal prism + 4x trigonal cupola + 1x truncated tetrahedron | |
53 | hexagonal antiprism prism | ?? | 12x trigonal prism + 2x hexagonal antiprism + 2x hexagonal prism | |
54 | hexagonal diprism | x6o2x4o | 6x cube + 4x hexagonal prism | |
55 | tetrahedral semiantiprism | xo3xx3ox | 6x tetrahedron + 8x trigonal cupola + 2x truncated tetrahedron | |
56 | tetrahedral quasicupola | xx3xo3oo | (1+4)x tetrahedron + 4x trigonal cupola + 1x truncated tetrahedron | |
57 | truncated tetrahedron prism | x3x3o2x | 4x trigonal prism + 4x hexagonal prism + 2x truncated tetrahedron | |
58 | K4.58 | xox8oxo&#x | 8x tetrahedron + 8x square pyramid + 2x octagonal antiprism + 1x octagonal prism | |
59 | 8,3-duoprism | x8o2x3o | 8x trigonal prism + 3x octagonal prism | |
60 | snub cube prism | s4s3s2x | (8+24)x trigonal prism + 6x cube + 2x snub cube | |
61 | staurohedral mesocupola | xo4ox3xo | 8x octahedron + 12x square pyramid + 6x square antiprism + 1x cuboctahedron + 1x rhombicuboctahedron | |
62 | K4.62 | ?? | 4x octahedron + (4+4+4)x square pyramid + (1+4)x square antiprism + 1x cuboctahedron + 1x elongated square cupola + 1 square cupola | |
63 | K4.63 | ?? | (4+8)x square pyramid + 4x square antiprism + 1x cuboctahedron + 2x square cupola + 1x octagonal prism | |
64 | square gyrobicupolic ring | xxo4oxx&#x | 8x square pyramid + 1x square antiprism + 2x square cupola | |
65 | octagonal antiprism prism | ?? | 16x trigonal prism + 2x octagonal antiprism + 2x octagonal prism | |
66 | rhombicuboctahedral prism | x4o3x2x | 8x trigonal prism + (6+12)x cube + 2x rhombicuboctahedron | |
67 | elongated square gyrobicupola prism | ?? | 8x trigonal prism + (2+8+8)x cube + 2x elongated square gyrobicupola | |
68 | elongated square cupola prism | ?? | 4x trigonal prism + (1+4+4+4)x cube + 2x elongated square cupola + 1x octagonal prism | |
69 | square cupola prism | xx4xo2xx | 4x trigonal prism + (1+4)x cube + 2x square cupola + 1x octagonal prism | |
70 | octagonal diprism | x8o2x4o | 8x cube + 4x octagonal prism | |
71 | cubic pericupola | xx4oo3ox | 8x tetrahedron + 12x trigonal prism + (1+6)x cube + 1x rhombicuboctahedron | |
72 | K4.72 | ?? | 4x tetrahedron + (4+4)x trigonal prism + (1+1+4)x cube + 1x elongated square cupola + 1 square cupola | |
73 | square orthobicupolic ring | xx4xo2ox | 4x tetrahedron + 2x square pyramid + 4x trigonal prism + 1x cube | |
74 | dodecahedron prism | x5o3o2x | 12x pentagonal prism + 2x dodecahedron | |
75 | octahedral semipericupola | xx3xo4ox | 12x trigonal prism + 6x square antiprism + 8x trigonal cupola + 1x rhombicuboctahedron + 1x truncated octahedron | |
76 | tetrahedral canticupola | xx3xx3xo | 6x trigonal prism + 4x trigonal cupola + 4x hexagonal prism + 1 truncated tetrahedron + 1 truncated octahedron | |
77 | dodecahedral semicupola | xo5ox3oo | 20x tetrahedron + 12x pentagonal antiprism + 1x dodecahedron + 1x icosidodecahedron | |
78 | rhodohedral antiprism | xo5oo3ox | (20+30)x tetrahedron + 1x icosahedron + 12x pentagonal pyramid + 1x dodecahedron | |
79 | K4.79 | ?? | (5+5+5+5+5+5+10)x tetrahedron + 1x gyroelongated pentagonal pyramid + (1+5+5)x pentagonal pyramid + 1x pentagonal antiprism + 1x dodecahedron | |
80 | pentagonal antiprism pyramid | ?? | 10x tetrahedron + 2x pentagonal pyramid + 1x pentagonal antiprism | |
81 | K4.81 | ?? | (10+10+10)x tetrahedron + 10x pentagonal pyramid + (1+2)x pentagonal antiprism + 1x dodecahedron | |
82 | K4.82 | ?? | (1+1+2+2+2+2+4+4+4+4+4)x tetrahedron + (2+2+2+4)x pentagonal pyramid + 2x pentagonal antiprism + 1x metabidiminished icosahedron + 1x dodecahedron | |
83 | K4.83 | ?? | (1+1+3+3+3+3+6)x tetrahedron + (3+3+3)x pentagonal pyramid + 3x pentagonal antiprism + 1x tridiminished icosahedron + 1x dodecahedron | |
84 | icosahedron pyramid | xo3oo5oo | 20x tetrahedron + 1x icosahedron | |
85 | gyroelongated pentagonal pyramid pyramid | ?? | (5+5+5)x tetrahedron + 1x gyroelongated pentagonal pyramid + 1x pentagonal pyramid | |
86 | pentagonal dipyramid | xo5oo2ox | 5x tetrahedron + 2x pentagonal pyramid | |
87 | metabidiminished icosahedron pyramid | ?? | (2+2+2+4)x tetrahedron + 2x pentagonal pyramid + 1x metabidiminished icosahedron | |
88 | tridiminished icosahedron pyramid | ?? | (1+1+3)x tetrahedron + 3x pentagonal pyramid + 1x tridiminished icosahedron | |
89 | truncated octahedron prism | x3x4o2x | 6x cube + 8x hexagonal prism + 2x truncated octahedron | |
90 | icosidodecahedron prism | ?? | 20x trigonal prism + 12x pentagonal prism + 2x icosidodecahedron | |
91 | orthobirotunda prism | ?? | (10+10)x trigonal prism + (2+10)x pentagonal prism + 2x orthobirotunda | |
92 | rotunda prism | ?? | (5+5)x trigonal prism + (1+5)x pentagonal prism + 2x rotunda + 1x decagonal prism | |
93 | K4.93 | xox10oxo&#x | 10x tetrahedron + 10x square pyramid + 2x decagonal antiprism + 1x decagonal prism | |
94 | 10,3-duoprism | x10o2x3o | 10x trigonal prism + 3x decagonal prism | |
95 | octahedral semimesocupola | xo3xx4oo | 6x cube + 1x cuboctahedron + 8x trigonal cupola + 1x truncated octahedron | |
96 | decagonal antiprism prism | ?? | 20x trigonal prism + 2x decagonal antiprism + 2x decagonal prism | |
97 | decagonal diprism | x10o2x4o | 10x cube + 4x decagonal prism | |
98 | staurohedral semiantiprism | xo4xx3ox | 12x tetrahedron + 8x trigonal cupola + 6x square cupola + 1x truncated octahedron + 1x truncated cube | |
99 | truncated cube prism | x4x3o2x | 8x trigonal prism + 6x octagonal prism + 2x truncated cube | |
100 | cubic semipericupola | xx4xo3ox | 8x octahedron + 12x trigonal prism + 1x rhombicuboctahedron + 6x square cupola + 1x truncated cube | |
101 | K4.101 | ?? | 4x octahedron + (4+4)x square pyramid + (4+4+4)x trigonal prism + 1x elongated square gyrobicupola + (1+1+4)x square cupola + 1x truncated cube | |
102 | K4.102 | ?? | (8+8)x square pyramid + (4+8)x trigonal prism + 1x rhombicuboctahedron + (2+4)x square cupola + 1x truncated cube | |
103 | K4.103 | ?? | 4x octahedron + 4x square pyramid + (4+4)x triangular prism + 1x elongated square cupola + (1+4)x square cupola + 1x octagonal prism + 1x truncated cube | |
104 | K4.104 | ?? | (4+4+4)x square pyramid + (4+4)x trigonal prism + 1x elongated square cupola + (1+4)x square cupola + 1x octagonal prism + 1x truncated cube | |
105 | square magnabicupolic ring | xx4xo2xo | 4x square pyramid + 4x trigonal prism + 2x square cupola + 1x octagonal prism | |
106 | K4.106 | ?? | 8x square pyramid + 4x trigonal prism + 4x square cupola + (1+2)x octagonal prism + 1x truncated cube | |
107 | octahedral pericupola | xx3oo4ox | 1x octahedron + 6x square pyramid + (8+12)x trigonal prism + 1x rhombicuboctahedron | |
108 | K4.108 | ?? | (1+1+4)x square pyramid + (4+4+4)x trigonal prism + 1x elongated square cupola + 1x square cupola | |
109 | K4.109 | ?? | 8x square pyramid + 2x trigonal prism + 2x square cupola | |
110 | snub dodecahedron prism | s5s3s2x | (20+60)x trigonal prism + 12x pentagonal prism + 2x snub dodecahedron | |
111 | rhombicosidodecahedron prism | x5o3x2x | 20x trigonal prism + 30x cube + 12x pentagonal prism + 2x rhombicosidodecahedron | |
112 | gyrated rhombicosidodecahedron prism | ?? | (5+5+5+5)x trigonal prism + (5+5+5+5+10)x cube + (1+1+5+5)x pentagonal prism + 2x gyrated rhombicosidodecahedron | |
113 | parabigyrated rhombicosidodecahedron prism | ?? | (10+10)x trigonal prism + (10+10+10)x cube + (2+10)x pentagonal prism + 2x parabigyrated rhombicosidodecahedron | |
114 | metabigyrated rhombicosidodecahedron | ?? | (2+2+2+2+4+4+4)x trigonal prism + (1+1+2+2+4+4+4+4+4+4)x cube + (2+2+2+2+4)x pentagonal prism + 2x metabigyrated rhombicosidodecahedron | |
115 | trigyrated rhombicosidodecahedron | ?? | (1+1+3+3+6+6)x trigonal prism + (3+3+3+3+6+6+6)x cube + (3+3+3+3)x pentagonal prism + 2x trigyrated rhombicosidodecahedron | |
116 | diminished rhombicosidodecahedron prism | ?? | (5+5+5)x trigonal prism + (5+5+5+10)x cube + (1+5+5)x pentagonal prism + 1x decagonal prism + 2x diminished rhombicosidodecahedron | |
117 | pentagonal cupola prism | xx5xo2xx | 5x trigonal prism + 5x cube + 1x pentagonal prism + 1x decagonal prism + 2x pentagonal cupola | |
118 | gyrated paradiminished rhombicosidodecahedron prism | ?? | (5+5+5)x trigonal prism + (5+5+5+10)x cube + (1+5+5)x pentagonal prism + 1x decagonal prism + 2x gyrated paradiminished rhombicosidodecahedron | |
119 | gyrated metadiminished rhombicosidodecahedron prism | ?? | (1+1+1+2+2+2+2+2+2)x trigonal prism + (1+1+1+2+2+2+2+2+2+2+2+2+2+2)x cube + (1+1+1+2+2+2+2)x pentagonal prism + 1x decagonal prism + 2x gyrated metadiminished rhombicosidodecahedron | |
120 | bigyrated diminished rhombicosidodecahedron prism | ?? | (1+1+1+2+2+2+2+2+2)x trigonal prism + (1+1+1+2+2+2+2+2+2+2+2+2+2+2)x cube + (1+1+1+2+2+2+2)x pentagonal prism + 1x decagonal prism + 2x bigyrated diminished rhombicosidodecahedron | |
121 | parabidiminished rhombicosidodecahedron prism | ?? | 10x trigonal prism + (10+10)x cube + 10x pentagonal prism + 2x decagonal prism + 2x parabidiminished rhombicosidodecahedron | |
122 | metabidiminished rhombicosidodecahedron prism | ?? | (2+2+2+4)x trigonal prism + (1+1+2+4+4+4+4)x cube + (2+2+2+4)x pentagonal prism + 2x decagonal prism + 2x metabidiminished rhombicosidodecahedron | |
123 | gyrated bidiminished rhombicosidodecahedron prism | ?? | (1+1+1+1+2+2+2)x trigonal prism + (1+1+1+1+2+2+2+2+2+2+2+2+2)x cube + (1+1+1+1+2+2+2)x pentagonal prism + 2x decagonal prism + 2x gyrated bidiminished rhombicosidodecahedron | |
124 | tridiminished rhombicosidodecahedron prism | ?? | (1+1+3)x trigonal prism + (3+3+3+6)x cube + (3+3+3)x pentagonal prism + 3x decagonal prism + 2x tridiminished rhombicosidodecahedron | |
125 | truncated cuboctahedron prism | x4x3x2x | 12x cube + 8x hexagonal prism + 6x octagonal prism + 2x truncated cuboctahedron | |
126 | icosahedral semipericupola | xx3xo5ox | 30x trigonal prism + 12x pentagonal antiprism + 20x trigonal cupola + 1x rhombicosidodecahedron + 1x truncated icosahedron | |
127 | truncated icosahedron prism | x3x5o2x | 12x pentagonal prism + 20x hexagonal prism + 2x truncated icosahedron | |
128 | cubic canticupola | xx4xx3ox | 12x trigonal prism + 8x trigonal cupola + 6x octagonal prism + 1x truncated cube + 1x truncated cuboctahedron | |
129 | cubic semimesocupola | xo4xx3oo | 8x trigonal prism + 1x cuboctahedron + 6x square cupola + 1x truncated cube | |
130 | truncated dodecahedron prism | x5x3o2x | 20x trigonal prism + 12x decagonal prism + 2x truncated dodecahedron | |
131 | rhodohedral mesocupola | xo5ox3xo | 20x octahedron + 30x square pyramid + 12x pentagonal antiprism + 1x icosidodecahedron + 1x rhombicosidodecahedron | |
132 | K4.132 | ?? | (5+5+5)x octahedron + (5+5+5+5+10)x square pyramid + (1+5+5)x pentagonal antiprism + 1x icosidodecahedron + 1x diminished rhombicosidodecahedron + 1x pentagonal cupola | |
133 | pentagonal gyrobicupolic ring | xxo5oxx&#x | 10x square pyramid + 1x pentagonal antiprism + 2x pentagonal cupola | |
134 | K4.134 | ?? | 10x octahedon + (10+10+10)x square pyramid + 10x pentagonal antiprism + 1x icosidodecahedron + 2x pentagoal cupola + 1x parabidiminished rhombicosidodecahedron | |
135 | K4.135 | ?? | (2+2+2+4)x octahedron + (1+1+2+2+4+4+4+4+4+4)x square pyramid + (2+2+2+4)x pentagonal antiprism + 1x icosidodecahedron + 2x pentagonal cupola + 1x metabidiminished rhombicosidodecahedron | |
136 | K4.136 | ?? | (1+1+3)x octahedron + (3+3+3+3+6+6+6)x square pyramid + (3+3+3)x pentagonal antiprism + 1x icosidodecahedron + 3x pentagonal cupola + 1x tridiminished rhombicosidodecahedron | |
137 | K4.137 | xo3ox5oo | 20x octahedron + 1x icosahedron + 12x pentagonal pyramid + 1x icosidodecahedron | |
138 | K4.138 | ?? | (5+5+5)x octahedron + 5x square pyramid + 1x gyroelongated pentagonal pyramid + (1+5+5)x pentagonal pyramid + 1x pentagonal prism + 1x icosidodecahedron | |
139 | K4.139 | ?? | 5x octahedron + 5x square pyramid + (1+1+5)x pentagonal pyramid + 1x pentagonal rotnda +1x pentagonal cupola | |
140 | K4.140 | ?? | (5+5)x octahedron + 5x square pyramid + 1x gyroelongated pentagonal pyramid + (1+5)x pentagonal pyramid + 1x pentagonal rotunda + 1x pentagonal cupola | |
141 | pentagonal prism pyramid | xox5ooo&#x | 5x square pyramid + 2x pentagonal pyramid + 1x pentagonal prism | |
142 | K4.142 | ?? | 10x octahedron + 10x square pyramid + 10x pentagonal pyramid + 1x pentagonal antiprism + 2x pentagonal prism + 1x icosidodecahedron | |
143 | K4.143 | ?? | (2+2+2+4)x octahedron +(2+4+4)x square pyramid + (2+2+2+4)x pentagonal pyramid + 1x metabidiminished icosahedron + 1x pentagonal prism + 1x icosidodecahedron | |
144 | K4.144 | ?? | 5x octahedron + (5+5)x square pyramid + 5x pentagonal pyramid +1x pentagonal antiprism + 1x pentagonal prism + 1x pentagonal rotunda + 1x pentagonal cupola | |
145 | K4.145 | ?? | (1+1+2+2)x octahedron + (2+2+2+2)x square pyramid + (1+2+2)x pentagonal pyramid + 1x metabidiminished icosahedron + 1x pentagonal prism + 1x pentagonal rotunda + 1x pentagonal cupola | |
146 | K4.146 | ?? | (5+5)x square pyramid + 5x pentagonal pyramid + 1x pentagonal prism + 1x rotunda +1x pentagonal cupola | |
147 | K4.147 | ?? | (1+1+3)x octahedron + (3+6+6)x square pyramid + (3+3+3)x pentagonal pyramid + 1x tridiminished icosahedron + 3x pentagonal prism + 1x icosidodecahedron | |
148 | K4.148 | ?? | (1+1)x octahedron + (1+2+2+2+2+2)x square pyramid + (1+1+2)x pentagonal pyramid + 1x tridiminished icosahedron + 2x pentagonal prism + 1x pentagonal rotunda + 1x pentagonal cupola |
(To be completed)