User:Double sharp/Uniform polychora

Source: Wikipedia, the free encyclopedia.

This lists the convex uniform polychora in Bowers' and Johnson's names. The left # column is Bowers' numbering; the right # is Olshevsky's (and Wikipedia's).

# Bowers acronym Bowers-style name[note 1] Johnson-style name[note 2] #
Category 1: Regulars
1 Pen Pentachoron 5-cell 1
2 Tes Tesseract Tesseract 10
3 Hex Hexadecachoron 16-cell 12
4 Ico Icositetrachoron 24-cell 22
5 Hi Hecatonicosachoron 120-cell 32
6 Ex Hexacosichoron 600-cell 35
Category 2: Truncates
18 Tip Truncated pentachoron Truncated 5-cell 3
19 Tat Truncated tesseract Truncated tesseract 13
20 Thex Truncated hexadecachoron
Truncated 16-cell
17
21 Tico Truncated icositetrachoron
Truncated 24-cell
24
22 Thi Truncated hecatonicosachoron
Truncated 120-cell
36
23 Tex Truncated hexacosichoron
Truncated 600-cell
41
Category 3: Triangular Rectates
39 Rap Rectified pentachoron Rectified 5-cell 2
42 Rit Rectified tesseract Rectified tesseract 11
45 Rico Rectified icositetrachoron Rectified 24-cell 23
48 Rahi Rectified hecatonicosachoron Rectified 120-cell 33
Category 5: Pentagonal Rectates
73 Rox Rectified hexacosichoron Rectified 600-cell 34
Category 6: Sphenoverts
133 Srip Small rhombated pentachoron Cantellated 5-cell 4
140 Srit Small rhombated tesseract Cantellated tesseract 14
151 Srico Small rhombated icositetrachoron
Cantellated 24-cell
25
158 Srahi Small rhombated hecatonicosachoron Cantellated 120-cell 37
165 Srix Small rhombated hexacosichoron
Cantellated 600-cell
40
Category 7: Bitruncates
298 Deca Decachoron
Bitruncated 5-cell
6
299 Tah Tesseractihexadecachoron
Bitruncated tesseract
16
300 Cont Tetracontoctachoron
Bitruncated 24-cell
27
301 Xhi Hexacosihecatonicosachoron
Bitruncated 120-cell
39
Category 8: Great Rhombates
307 Grip Great rhombated pentachoron
Cantitruncated 5-cell
7
308 Grit Great rhombated tesseract
Cantitruncated tesseract
18
309 Grico Great rhombated icositetrachoron
Cantitruncated 24-cell
28
310 Grahi Great rhombated hecatonicosachoron
Cantitruncated 120-cell
42
311 Grix Great rhombated hexacosichoron
Cantitruncated 600-cell
45
Category 9: Omnitruncates
330 Gippid Great prismatodecachoron
Omnitruncated 5-cell
9
331 Gidpith Great disprismatotesseractihexadecachoron
Omnitruncated tesseract
21
332 Gippic Great prismatotetracontoctachoron
Omnitruncated 24-cell
30
333 Gidpixhi Great disprismatohexacosihecatonicosachoron
Omnitruncated 120-cell
46
Category 10: Prismatorhombates
352 Prip Prismatorhombated pentachoron
Runcitruncated 5-cell
8
355 Prit Prismatorhombated tesseract
Runcitruncated 16-cell
20
358 Proh Prismatorhombated hexadecachoron
Runcitruncated tesseract
19
361 Prico Prismatorhombated icositetrachoron
Runcitruncated 24-cell
29
364 Prahi Prismatorhombated hecatonicosachoron
Runcitruncated 600-cell
43
367 Prix Prismatorhombated hexacosichoron
Runcitruncated 120-cell
44
Category 11: Antipodiumverts
442 Spid Small prismatodecachoron Runcinated 5-cell 5
447 Sidpith Small disprismatotesseractihexadecachoron
Runcinated tesseract
15
454 Sidpixhi Small disprismatohexacosihecatonicosachoron
Runcinated 120-cell
38
Category 13: Spic and Giddic Regiments
512 Spic Small prismatotetracontoctachoron
Runcinated 24-cell
26
Category 19: Prisms
889 Tepe Tetrahedral prism Tetrahedral prism 48
890 Ope Octahedral prism Octahedral prism 51
891 Dope Dodecahedral prism Dodecahedral prism 57
892 Ipe Icosahedral prism
Icosahedral prism
59
898 Tuttip Truncated tetrahedral prism
Truncated tetrahedral prism
49
899 Ticcup Truncated cubic prism
Truncated cubic prism
53
900 Tope Truncated octahedral prism
Truncated octahedral prism
54
901 Tiddip Truncated dodecahedral prism
Truncated dodecahedral prism
60
902 Tipe Truncated icosahedral prism
Truncated icosahedral prism
62
908 Cope Cuboctahedral prism
Cuboctahedral prism
50
909 Iddip Icosidodecahedral prism
Icosidodecahedral prism
58
923 Sircope Small rhombicuboctahedral prism Rhombicuboctahedral prism 52
926 Sriddip Small rhombicosidodecahedral prism
Rhombicosidodecahedral prism
61
944 Gircope Great rhombicuboctahedral prism
Truncated cuboctahedral prism
55
945 Griddip Great rhombicosidodecahedral prism
Truncated icosidodecahedral prism
63
951 Sniccup Snub cubic prism
Snub cubic prism
56
952 Sniddip Snub dodecahedral prism
Snub dodecahedral prism
64
Category 20: Miscellaneous
963 Gap Grand antiprism Grand antiprism 47
969 Sadi Snub disicositetrachoron Snub 24-cell 31

Notes

  1. ^ (analogous to Kepler's names for the Archimedean solids)
  2. ^ (used on Wikipedia; not all are Johnson's)