Facet layout
| Name
| Petrie order
| SSC2
| Cells
| Faces
| Edges
| Vertices
| Alternation
| Dual
|
| Pentachoron | 5,0 | Kp1 | 5 | 10 | 10 | 5 | None | Self-dual
|
| Hexadecachoron | 8,0 | Ke8 | 16 | 32 | 24 | 8 | None | Tesseract
|
| Hexacosichoron | 30,30,30,30,0 | Ks8 | 600 | 1200 | 720 | 120 | None | Hecatonicosachoron
|
| Icositetrachoron | 12,12,0 | Kk1 | 24 | 96 | 96 | 24 | None | Self-dual
|
| Tesseract | 8,8,0 | Ke1 | 8 | 24 | 32 | 16 | Hexadecachoron | Hexadecachoron
|
| Hecatonicosachoron | 12 rings | Ks1 | 120 | 720 | 1200 | 600 | None | Hexacosichoron
|
| Pentachoric rectate | Unknown | Kp6 | 10 | 40 | 60 | 30 | None | Unknown
|
| Icositetrachoric rectate | Unknown | Kp6 | 48 | 336 | 576 | 288 | None | Unknown
|
| Pentachoric hemicate | Unknown | Kp2 | 10 | 30 | 30 | 10 | None | Unknown
|
| Tesseric hemicate | Unknown | Ke2 | 24 | 88 | 96 | 32 | None | Unknown
|
| Hecatonicosachoric hemicate | Unknown | Ks2 | 720 | 3120 | 3600 | 1200 | None | Unknown
|
| Icositetrachoric hemicate | Unknown | Kk2 | 48 | 240 | 288 | 96 | None | Unknown
|
| Tetrahedral prism | Unknown | +Kt1 | 6 | 15 | 16 | 8 | None | Unknown
|
| Pentachoric cantellate | Unknown | Kp9 | 30 | 70 | 60 | 20 | None | Unknown
|
| Octahedral prism | Unknown | +Ko4 | 10 | 28 | 30 | 12 | None | Unknown
|
| Icositetrachoric cantellate | Unknown | Kk9 | 240 | 672 | 576 | 144 | None | Unknown
|
| Icosahedral prism | Unknown | +Ki4 | 22 | 70 | 72 | 24 | None | Unknown
|
| Dodecahedral prism | Unknown | +Ki1 | 14 | 54 | 80 | 40 | None | Unknown
|
| Pentachoric truncate | Unknown | Kp3 | 10 | 30 | 40 | 20 | None | Unknown
|
| Hexadecachoric truncate | Unknown | Ke12 | 24 | 96 | 120 | 48 | None | Unknown
|
| Hexacosichoric truncate | Unknown | Ks12 | 720 | 3600 | 4320 | 1440 | None | Unknown
|
| Tesseric truncate | Unknown | Ke3 | 24 | 88 | 128 | 64 | None | Unknown
|
| Hecatonicosachoric truncate | Unknown | Ks3 | 720 | 3120 | 4800 | 2400 | None | Unknown
|
| Icositetrachoric truncate | Unknown | Kk3 | 48 | 240 | 384 | 192 | Icositetrachoric snub | Unknown
|
| 3,5-duoprism | Unknown | G3xG5 | 8 | 23 | 30 | 15 | None | Unknown
|
| Tesseric rectate | Unknown | Ke6 | 24 | 120 | 192 | 96 | None | Unknown
|
| Hecatonicosachoric rectate | Unknown | Ks6 | 720 | 4320 | 7200 | 3600 | None | Unknown
|
| Pentachoric omnitruncate | Unknown | Kp15 | 30 | 150 | 240 | 120 | None | Unknown
|
| Icositetrachoric omnitruncate | Unknown | Kk15 | 240 | 1392 | 2304 | 1152 | None | Unknown
|
| Cuboctahedral prism | Unknown | +Ko2 | 16 | 52 | 60 | 24 | None | Unknown
|
| Icosidodecahedral prism | Unknown | +Ki2 | 34 | 124 | 150 | 60 | None | Unknown
|
| Grand antiprism | Unknown | Unknown | 320 | 720 | 500 | 100 | None | Unknown
|
| Pentachoric omnihemate | Unknown | Kp5 | 20 | 80 | 90 | 30 | None | Unknown
|
| Hexacosichoric omnihemate | Unknown | Ks10 | 1440 | 8640 | 10800 | 3600 | None | Unknown
|
| Icositetrachoric omnihemate | Unknown | Ke5 | 56 | 248 | 288 | 96 | None | Unknown
|
| Tesseric omnihemate | Unknown | Kk5 | 144 | 720 | 864 | 288 | None | Unknown
|
| Hecatonicosachoric omnihemate | Unknown | Ks5 | 1920 | 9120 | 10800 | 3600 | None | Unknown
|
| Tetrahedral truncate prism | Unknown | +Kt3 | 10 | 34 | 48 | 24 | None | Unknown
|
| Pentachoric canticate | Unknown | Kp7 | 20 | 80 | 120 | 60 | None | Unknown
|
| Hexacosichoric canticate | Unknown | Ks14 | 1440 | 8640 | 14400 | 7200 | None | Unknown
|
| Icositetrachoric canticate | Unknown | Kk7 | 144 | 720 | 1152 | 576 | None | Unknown
|
| Tesseric canticate | Unknown | Ke7 | 56 | 248 | 384 | 192 | None | Unknown
|
| Hecatonicosachoric canticate | Unknown | Ks7 | 1920 | 9120 | 14400 | 7200 | None | Unknown
|
| Tesseric cantellate | Unknown | Ke9 | 80 | 208 | 192 | 64 | None | Unknown
|
| Hecatonicosachoric cantellate | Unknown | Ks9 | 2640 | 7440 | 7200 | 2400 | None | Unknown
|
| Pentachoric runcicate | Unknown | Kp11 | 30 | 120 | 150 | 60 | None | Unknown
|
| Hexadecachoric runcicate | Unknown | Ke13 | 80 | 368 | 480 | 192 | None | Unknown
|
| Hexacosichoric runcicate | Unknown | Ks13 | 2640 | 13440 | 18000 | 7200 | None | Unknown
|
| Icositetrachoric runcicate | Unknown | Kk11 | 240 | 1104 | 1440 | 576 | None | Unknown
|
| Tesseric runcicate | Unknown | Ke11 | 80 | 368 | 480 | 192 | None | Unknown
|
| Hecatonicosachoric runcicate | Unknown | Ks11 | 2640 | 13440 | 18000 | 7200 | None | Unknown
|
| Cubic snub prism | Unknown | +Ko0 | 40 | 132 | 144 | 48 | None | Unknown
|
| Cuboctahedral truncate prism | Unknown | +Ko7 | 28 | 124 | 192 | 96 | None | Unknown
|
| Tesseric omnitruncate | Unknown | Ke15 | 80 | 464 | 768 | 384 | None | Unknown
|
| Hecatonicosachoric omnitruncate | Unknown | Ks15 | 2640 | 17040 | 28800 | 14400 | None | Unknown
|