List of Uniform Polychora

This is a list of uniform polychora, plus some of the infinite duoprism and antiduoprism series. As of January 2024, there are 2191 known uniform polychora (excluding the infinite duoprism and antiduoprism families), most of which were discovered by Jonathan Bowers and George Olshevsky. The polychora are listed by the categories on Bowers' website. Each of the polychora's corresponding Bowers acronyms are bolded and in parentheses. Coxeter–Dynkin diagrams of the polytopes (if applicable) are also displayed.

## Category 1: Regulars (plus the Tesseractihemioctachoron) (1-17)

### Convex Regular Polychora (1-6)

* 1. Pentachoron (**pen**),
* 2. Tesseract (**tes**),
* 3. Hexadecachoron (**hex**),
* 4. Icositetrachoron (**ico**),
* 5. Hecatonicosachoron (**hi**),
* 6. Hexacosichoron (**ex**),

### Self-Intersecting Regular Polychora (7-16)

* 7. Faceted hexacosichoron (**fix**),
* 8. Great hecatonicosachoron (**gohi**),
* 9. Grand hecatonicosachoron (**gahi**),
* 10. Small stellated hecatonicosachoron (**sishi**),
* 11. Great grand hecatonicosachoron (**gaghi**),
* 12. Great stellated hecatonicosachoron (**gishi**),
* 13. Grand stellated hecatonicosachoron (**gashi**),
* 14. Great faceted hexacosichoron (**gofix**),
* 15. Grand hexacosichoron (**gax**),
* 16. Great grand stellated hecatonicosachoron (**gogishi**),

### Tesseractihemioctachoron (17)

* 17. Tesseractihemioctachoron (**tho**),  (2tho)

## Category 2: Truncates (18-38)

### Convex Truncates (18-23)

* 18. Truncated pentachoron (**tip**),
* 19. Truncated tesseract (**tat**),
* 20. Truncated hexadecachoron (**thex**),
* 21. Truncated icositetrachoron (**tico**),
* 22. Truncated hecatonicosachoron (**thi**),
* 23. Truncated hexacosichoron (**tex**),

### Star Truncates (24-29)

* 24. Truncated faceted hexacosichoron (**tiffix**),
* 25. Truncated great hecatonicosachoron (**tighi**),
* 26. Truncated grand hecatonicosachoron (**taghi**),
* 27. Truncated great grand hecatonicosachoron (**tigaghi**),
* 28. Truncated great faceted hexacosichoron (**tigfix**),
* 29. Truncated grand hexacosichoron (**taggix**),

### Truncated tesseractihemioctachoron (30)

* 30. Truncated tesseractihemioctachoron (**titho**),  (2titho)

### Ditrigonary Truncates (31-33)

* 31. Truncated small ditrigonary hexacosihecatonicosachoron (**tissidtixhi**)
* 32. Truncated ditrigonary dishecatonicosachoron (**tidtidohi**)
* 33. Truncated great ditrigonary hexacosihecatonicosachoron (**tiggidtixhi**)

### Quasitruncates (34-38)

* 34. Quasitruncated tesseract (**quitit**),
* 35. Quasitruncated small stellated hecatonicosachoron (**quit sishi**),
* 36. Quasitruncated great stellated hecatonicosachoron (**quit gishi**),
* 37. Quasitruncated grand stellated hecatonicosachoron (**quit gashi**),
* 38. Quasitruncated great grand stellated hecatonicosachoron (**quit gogishi**),

## Category 3: Triangular Rectates (39-59)

### Rectified pentachoron regiment (39-41)

* 39. Rectified pentachoron (**rap**),
* 40. Facetorectified pentachoron (**firp**),  (2firp)
* 41. Pentintercepted pentachoron (**pinnip**)

### Rectified tesseract regiment (42-44)

* 42. Rectified tesseract (**rit**),
* 43. Facetorectified tesseract (**firt**),
* 44. Hexadecintercepted tesseract (**hinnit**)

### Rectified icositetrachoron regiment (45-47)

* 45. Rectified icositetrachoron (**rico**),
* 46. Facetorectified icositetrachoron (**frico**),  (2frico)
* 47. Icositetrintercepted icositetrachoron (**ini**)

### Rectified hecatonicosachoron regiment (48-50)

* 48. Rectified hecatonicosachoron (**rahi**),
* 49. Facetorectified hecatonicosachoron (**fry**)
* 50. Small hecatonicosintercepted hecatonicosachoron (**shinhi**)

### Rectified small stellated hecatonicosachoron regiment (51-53)

* 51. Rectified small stellated hecatonicosachoron (**rasishi**)
* 52. Facetorectified small stellated hecatonicosachoron (**firsashi**)
* 53. Hecatonicosintercepted small stellated hecatonicosachoron (**hinhi**)

### Rectified great grand hecatonicosachoron regiment (54-56)

* 54. Rectified great grand hecatonicosachoron (**ragaghi**)
* 55. Facetorectified great grand hecatonicosachoron (**firgaghi**)
* 56. Medial hecatonicosintercepted great grand hecatonicosachoron (**mohiny**)

### Rectified great grand stellated hecatonicosachoron (57-59)

* 57. Rectified great grand stellated hecatonicosachoron (**rigogishi**)
* 58. Facetorectified great grand stellated hecatonicosachoron **(firgogishi)**
* 59. Great hecatonicosintercepted great grand stellated hecatonicosachoron **(gohiny)**

## Category 4: Icositetrachoron Regiment (4, 60-72)

### Have Full Icositetrachoric symmetry (4, 60)

* 4. **Icositetrachoron** **(ico)**,
* 60. Icositetrahemicositetrachoron **(ihi)**

### Have Full Hexadecachoric symmetry (61-66)

* 61. Octahemihexadecachoron **(oh)**
* 62. Small hexadecahemihexadecachoron **(shahoh)**
* 63. Hexadecahemihexadecachoron **(huhoh)**
* 64. Hexadecoctahemihexadecachoron **(hohoh)**
* 65. Octahexadecahemihexadecachoron **(ohuhoh)**
* 66. Great hexadecahemihexadecachoron **(ghahoh)**

### Have Full Demitesseractic symmetry (67-72)

* 67. Rectified tesseractihemioctachoron **(ratho)**
* 68. Octadishemioctachoron **(odho)**
* 69. Hexadecoctadishemioctachoron **(hodho)**
* 70. Hexadecoctihemihexadekintercepted hemioctachoron **(hoh honho)**
* 71. Disoctidishemioctintercepted hemioctachoron **(dod honho)**
* 72. Disoctahemihexadekintercepted hemioctachoron **(doh honho)**

## Category 5: Pentagonal Rectates (73-132)

### Rectified hexacosachoron regiment (73-87)

* 73. Rectified hexacosichoron **(rox)**
* 74. Rectified faceted hexacosichoron **(rofix)**
* 75. Small prismatohecatonicosachoron **(sophi)**
* 76. Small pentagonal retroprismatoverted dishecatonicosachoron **(sprapivady)**
* 77. Facetorectified hexacosichoron **(frox)**
* 78. Retroinverted hexacosihecatonicosachoron **(rixhi)**
* 79. Small retropental hecatonicosachoron **(sriphi)**
* 80. Invertipental hexacosidishecatonicosachoron **(ipixady)**
* 81. Polar facetopental prismatohexacosihecatonicosachoron **(lifpipixhi)**
* 82. Interceptipental hexacosidishecatonicosachoron **(nipixady)**
* 83. Small omnicircumfacetopental triakishecatonicosachoron **(som fapathi)**
* 84. Small omnifacetopental triakishecatonicosachoron **(sofapathi)**
* 85. Small circumfacetopental triakishecatonicosachoron **(smiffipathi)**
* 86. Pental prismatohecatonicosintercepted hecatonicosachoron **(paphiny)**
* 87. Small inverted retropental hecatonicosintercepted dishecatonicosachoron **(sirphinady)**

### Rectified great hecatonicosachoron regiment (88-102)

* 88. Rectified great hecatonicosachoron **(righi)**
* 89. Rectified grand hecatonicosachoron **(raghi)**
* 90. Pentagramal antiprismatoverted hexacosihecatonicosachoron **(papvixhi)**
* 91. Great pentagonal retroprismatoverted dishecatonicosachoron **(giprapivady)**
* 92. Facetorectified great hecatonicosachoron **(froghi)**
* 93. Retroinverted dishecatonicosachoron **(ridhei)**
* 94. Medial retropental hecatonicosachoron **(mriphi)**
* 95. Small invertipental triakishecatonicosachoron **(sipathi)**
* 96. Polar facetopental hexacosidishecatonicosachoron **(lifpixady)**
* 97. Small interceptipental triakishecatonicosachoron **(snipathi)**
* 98. Medial omnicircumfacetopental triakishecatonicosachoron **(mom fapathi)**
* 99. Great omnifacetopental triakishecatonicosachoron **(gofapathi)**
* 100. Medial circumfacetopental triakishecatonicosachoron **(mim fipathi)**
* 101. Pental hexacosihecatonicosaintercepted hecatonicosachoron **(pixhiny)**
* 102. Great inverted retropental hecatonicosaintercepted dishecatonicosachoron **(girphinady)**

### Rectified great stellated hecatonicosachoron regiment (103-117)

* 103. Rectified great stellated hecatonicosachoron **(ragishi)**
* 104. Rectified grand stellated hecatonicosachoron **(ragashi)**
* 105. Small pentagramal antiprismatoverted dishecatonicosachoron **(spapivady)**
* 106. Pentagonal retroprismatoverted hexacosihecatonicosachoron **(prap vixhi)**
* 107. Facetorectified great stellated hecatonicosachoron (**frogshi**)
* 108. Retroinverted hecatonicosahexacosichoron (**rihix**)
* 109. Great retropental hecatonicosachoron (**griphi**)
* 110. Medial invertipental triakishecatonicosachoron (**mipathi**)
* 111. Small polar facetopental triakishecatonicosachoron (**sliffipathi**)
* 112. Medial interceptipental triakishecatonicosachoron (**minnipathi**)
* 113. Great omnicircumfacetopental triakishecatonicosachoron (**gom fapathi**)
* 114. Omnifacetopental hexacosidishecatonicosachoron (**ofapaxady**)
* 115. Great circumfacetopental triakishecatonicosachoron (**gam fipathi**)
* 116. Small pental dishecatonicosaintercepted hecatonicosachoron (**spidhiny**)
* 117. Inverted retropental hexacosintercepted dishecatonicosachoron (**irp xanady**)

### Rectified great faceted hexacosichoron regiment (118-132)

* 118. Rectified great faceted hexacosichoron (**rigfix**)
* 119. Rectified grand hexacosichoron (**raggix**)
* 120. Great pentagramal antiprismatoverted dishecatonicosachoron **(gippapivady)**
* 121. Quasiprismatohecatonicosachoron (**quiphi**)
* 122. Facetorectified great faceted hexacosichoron (**frogfix**)
* 123. Retroinverted prismatohecatonicosachoron (**ripahi**)
* 124. Grand retropental hecatonicosachoron (**graphi**)
* 125. Great invertipental triakishecatonicosachoron (**gipathi**)
* 126. Great polar facetopental triakishecatonicosachoron (**gliffipathi**)
* 127. Great interceptipental triakishecatonicosachoron (**ganipathi**)
* 128. Omnicircumfacetopental hexacosidishecatonicosachoron (**omfapaxady**)
* 129. Omnifacetopental prismatohexacosihecatonicosachoron (**ofpipixhi**)
* 130. Circumfacetopental hexacosidishecatonicosachoron (**mif pixady**)
* 131. Great pental dishecatonicosintercepted hecatonicosachoron (**gipdohiny**)
* 132. Inverted retropental prismatointercepted dishecatonicosachoron (**irp panady**)

## Category 6: Sphenoverts (45-47, 133-297)

### Small rhombated pentachoron regiment (133-139)

* 133. Small rhombated pentachoron (**srip**, Cantellated pentachoron)
* 134. Retrosphenoverted trispentachoron (**rawvtip**)
* 135. Small rhombic dispentachoron (**sirdop**)
* 136. Pseudorhombic prismatopentachoron (**pirpop**)
* 137. Grand rhombic prismatopentachoron (**garpop**)
* 138. Prismatopentintercepted dispentachoron (**pippindip**)
* 139. Pentaintercepted prismatodispentachoron (**pinnipdip**)

### Small rhombated tesseract regiment (140-146)

* 140. Small rhombated tesseract (**srit**, cantillated tesseract)
* 141. Retrosphenoverted tesseractitesseractihexadecachoron (**rawvatoth**)
* 142. Small rhombic disoctachoron (**sirdo**)
* 143. Small pseudorhombic prismatotesseract (**spript**)
* 144. Grand rhombic prismatotesseract (**garpit**)
* 145. Prismatotesseractintercepted tesseractihexadecachoron (**pattinoth**)
* 146. Prismatointercepted prismatotesseractihexadecachoron (**pinpith**)

### Rectified icositetrachoron regiment (45-47, 147-150)

* 45. **Rectified icositetrachoron** (**rico**)
* 46. **Facetorectified icositetrachoron** (**frico**)
* 47. **Icositetrintercepted icositetrachoron** (**ini**)
* 147. Retrosphenoverted hexadecatesseractioctachoron (**rawvhitto**)
* 148. Small rhombic tesseractihexadecachoron (**sirth**)
* 149. Grand rhombic dishexadecachoron (**gardoh**)
* 150. Hexadecaintercepted prismatotesseractihexadecachoron (**hinpith**)

### Small rhombated icositetrachoron regiment (151-157)

* 151. Small rhombated icositetrachoron (**srico**, Cantillated icositetrachoron)
* 152. Retrosphenoverted trisicositetrachoron (**rawvaty**)
* 153. Small rhombic disicositetrachoron (**sirdi**)
* 154. Small pseudorhombic disicositetrachoron (**spirdy**)
* 155. Grand rhombic disicositetrachoron (**gardi**)
* 156. Disicositetraintercepted disicositetrachoron (**dindi**)
* 157. Icositetraintercepted prismatodisicositetrachoron (**inipdi**)

### Small rhombated hecatonicosachoron regiment (158-164)

* 158. Small rhombated hecatonicosachoron (**srahi**, Cantillated hecatonicosachoron)
* 159. Small retrosphenoverted hexacosadishecatonicosachoron (**srawvixady**)
* 160. Small rhombic dishecatonicosachoron (**sirdhi**)
* 161. Small pseudorhombic prismatohecatonicosachoron (**spriphi**)
* 162. Grand rhombic prismatohecatonicosachoron (**garphi**)
* 163. Prismatohecatonicosaintercepted hexacosihecatonicosachoron (**phinxhi**)
* 164. Prismatointercepted prismatohexacosihecatonicosachoron (**pinpixhi**)

### Small rhombated hexacosichoron regiment (165-171)

* 165. Small rhombated hexacosichoron (**srix**, Cantillated haxacontachoron)
* 166. Small retrosphenoverted hecatonicosihexacosihecatonicosachoron (**srawv hixhi**)
* 167. Rhombic small hexacosihecatonicosachoron (**rassixhi**)
* 168. Pseudorhombic small dishecatonicosachoron (**pirsady**)
* 169. Grand rhombic small hexacosihecatonicosachoron (**garsixhi**)
* 170. Small dishecatonicosaintercepted hexacosihecatonicosachoron (**sid hinxhi**)
* 171. Hecatonicosaintercepted prismatohexacosihecatonicosachoron (**hinpixhi**)

### Small rhombated facetted hexacosichoron regiment (172-178)

* 172. Small rhombated facetted hexacosichoron (**sirfix**, Cantellated icosahedral hecatonicosachoron)
* 173. Small retrosphenoverted trishecatonicosachoron (**srawvathi**)
* 174. Rhombic small hecatonicosahecatonicosachoron (**rashihy**)
* 175. Small pseudorhombic hecatonicosahecatonicosachoron (**sprahihy**)
* 176. Grand rhombic dishecatonicosachoron (**garady**)
* 177. Small dishecatonicosaintercepted dishecatonicosachoron (**sid hinady**)
* 178. Hecatonicosaintercepted prismatodishecatonicosachoron (**hinipady**)

### Small rhombated small stellated hecatonicosachoron regiment (179-185)

* 179. Small rhombated small stellated hecatonicosachoron (**sirsashi**, Stellacantellated hecatonicosachoron)
* 180. Medial retrosphenoverted hecatonicosihexacosihecatonicosachoron (**mrawv hixhi**)
* 181. Rhombic small hecatonicosahexacosichoron (**rashix**)
* 182. Pseudorhombic small hexacosihecatonicosachoron (**pirsixhi**)
* 183. Grand rhombic small dishecatonicosachoron (**garsady**)
* 184. Small hexacosihecatonicosaintercepted dishecatonicosachoron (**sixhinady**)
* 185. Small hecatonicosaintercepted prismatodishecatonicosachoron (**shinipady**)

### Small hecatonicosaintercepted prismatodishecatonicosachoron regiment (186-192)

* 186. Small rhombated great hecatonicosachoron (**sirghi**, Great cantellated hecatonicosachoron)
* 187. Small retrosphenoverted hecatonicosadishecatonicosachoron (**srawv hidy**)
* 188. Rhombic small dishecatonicosachoron (**rassady**)
* 189. Pseudorhombic small hecatonicosahexacosichoron (**pirshix**)
* 190. Grand rhombic small hecatonicosahexacosichoron (**garshix**)
* 191. Small hecatonicosahexacosiintercepted dishecatonicosachoron (**shixanady**)
* 192. Small hexacosiintercepted prismatodishecatonicosachoron (**sixnapady**)

### Small rhombated grand hecatonicosachoron regiment (193-199)

* 193. Small rhombated grand hecatonicosachoron (**sraghi**, Grand cantellated hecatonicosachoron)
* 194. Retrosphenoverted trishecatonicosachoron (**rawvathi**)
* 195. Small rhombic hecatonicosahecatonicosachoron (**sirhihy**)
* 196. Pseudorhombic dishecatonicosachoron (**pirdy**)
* 197. Grand rhombic hecatonicosahecatonicosachoron (**garhihy**)
* 198. Dishecatonicosaintercepted dishecatonicosachoron (**dohinady**)
* 199. Hecatonicosaintercepted hecatonicosaprismatohecatonicosachoron (**hinhiphi**)

### Small rhombated great grand hecatonicosachoron regiment (200-206)

* 200. Small rhombated great grand hecatonicosachoron (**sirgaghi**, Giant cantellated hecatonicosachoron)
* 201. Great retrosphenoverted hecatonicosahexacosihecatonicosachoron (**grawv hixhi**)
* 202. Rhombic great hecatonicosahexacosichoron (**raghix**)
* 203. Pseudorhombic great hexacosihecatonicosachoron (**pirgixhi**)
* 204. Grand rhombic great dishecatonicosachoron (**gargady**)
* 205. Great hexacosihecatonicosaintercepted dishecatonicosachoron (**gixhinady**)
* 206. Great hecatonicosaintercepted prismatodishecatonicosachoron (**ghinipady**)

### Small rhombated grand stellated hecatonicosachoron regiment (207-213)

* 207. Small rhombated grand stellated hecatonicosachoron (**sirgashi**, Grand stellicantellated hecatonicosachoron)
* 208. Great retrosphenoverted hecatonicosadishecatonicosachoron (**grawv hidy**)
* 209. Rhombic great dishecatonicosachoron (**raggady**)
* 210. Pseudorhombic great hecatonicosahexacosichoron (**pirghix**)
* 211. Grand rhombic great hecatonicosahexacosichoron (**garghix**)
* 212. Great hecatonicosahexacosiintercepted dishecatonicosachoron (**ghixanady**)
* 213. Great hexacosiintercepted prismatodishecatonicosachoron (**gixnapady**)

### Small rhombicated grand hexacosichoron regiment (214-220)

* 214. Small rhombated grand hexacosichoron (**sirgax**, Grand cantellated hexacosichoron)
* 215. Grand retrosphenoverted hecatonicosahexacosihecatonicosachoron (**garawv hixhi**)
* 216. Rhombic great hexacosihecatonicosachoron (**raggixhi**)
* 217. Pseudorhombic great dishecatonicosachoron (**pirgady**)
* 218. Grand rhombic great hexacosihecatonicosachoron (**gargixhi**)
* 219. Great dishecatonicosaintercepted hexacosihecatonicosachoron (**gid hinxhi**)
* 220. Hecatonicosaintercepted prismatohecatonicosahexacosichoron (**hin phix**)

### Sphenoverted tesseractitesseractihexadecachoron regiment (221-227)

* 221. Sphenoverted tesseractitesseractihexadecachoron (**wavitoth**)
* 222. Quasirhombated tesseract (**qrit**)
* 223. Great rhombic disoctachoron (**girdo**)
* 224. Great pseudorhombic prismatotesseract (**gapript**)
* 225. Grand quasirhombic prismatotesseract (**gaqript**)
* 226. Disprismatointercepted tesseractihexadecachoron (**dippanoth**)
* 227. Prismatointercepted tesseractitesseractihexadecachoron (**pinnatoth**)

### Sphenoverted trisicositetrachoron regiment (228-234)

* 228. Sphenoverted trisicositetrachoron (**wavaty**)
* 229. Quasirhombated icositetrachoron (**qrico**)
* 230. Great rhombic disicositetrachoron (**girdi**)
* 231. Great pseudorhombic disicositetrachoron (**gapirdy**)
* 232. Grand quasirhombic disicositetrachoron (**gaquerdy**)
* 233. Prismatoicositetraintercepted disicositetrachoron (**pindi**)
* 234. Icositetraintercepted trisicositetrachoron (**inti**)

### Small sphenoverted ditrigonal trishecatonicosachoron regiment (235-241)

* 235. Small sphenoverted ditrigonal trishecatonicosachoron (**swav ditathi**)
* 236. Great retrosphenoverted trishecatonicosachoron (**grawvathi**)
* 237. Small hecatonicosadishecatonicosachoron (**shidy**)
* 238. Small retrotrishecatonicosachoron (**sirthi**)
* 239. Small small dishecatonicosachoron (**sisady**)
* 240. Dishecatonicosaintercepted ditrigonal dishecatonicosachoron (**dohine dattidy**)
* 241. Small hecatonicosaintercepted trishecatonicosachoron (**shinathi**)

### Sphecnoverted hecatonicosadishexacosichoron regiment (242-248)

* 242. Sphenoverted hecatonicosadishexacosichoron (**wavhiddix**)
* 243. Retrosphenoverted ditrigonal hexacosidishecatonicosachoron (**rawvid tixady**)
* 244. Small hecatonicosahexacosihecatonicosachoron (**shixhi**)
* 245. Small retrohexacosidishecatonicosachoron (**sirxady**)
* 246. Small dishecatonicosachoron (**sidahi**)
* 247. Dishecatonicosaintercepted hecatonicosahexacosichoron (**dohinahix**)
* 248. Hecatonicosaintercepted hecatonicosadishexacosichoron (**hin hiddix**)

### Great sphenoverted ditrigonal trishecatonicosachoron regiment (249-255)

* 249. Great sphenoverted ditrigonal trishecatonicosachoron (**gwav ditathi**)
* 250. Great retrosphenoverted hexacosidishecatonicosachoron (**grawvixady**)
* 251. Great hexacosidishecatonicosachoron (**gixady**)
* 252. Great retrohecatonicosahexacosihecatonicosachoron (**girhixhi**)
* 253. Great great dishecatonicosachoron (**gigady**)
* 254. Hexacosihecatonicosaintercepted ditrigonal dishecatonicosachoron (**xhin dittady**)
* 255. Medial hecatonicosaintercepted trishecatonicosachoron (**mohinathi**)

### Small sphenoverted hexacosidishecatonicosachoron regiment (256-262)

* 256. Small sphenoverted hexacosidishecatonicosachoron (**swavixady**)
* 257. Small retrosphenoverted ditrigonal trishecatonicosachoron (**srawv ditathi**)
* 258. Small hexacosidishecatonicosachoron (**sixady**)
* 259. Small retrohecatonicosahexacosihecatonicosachoron (**sirhixhi**)
* 260. Small great dishecatonicosachoron (**sigady**)
* 261. Great dishecatonicosaintercepted dishecatonicosachoron (**gid hinady**)
* 262. Hecatonicosaintercepted ditrigonal hexacosidishecatonicosachoron (**hind tixady**)

### Sphenoverted ditrigonal hexacosidishecatonicoschoron regiment (263-269)

* 263. Sphenoverted ditrigonal hexacosidishecatonicosachoron (**wavdatixady**)
* 264. Retrosphenoverted hecatonicosadishexacosichoron (**rawvhiddix**)
* 265. Great hecatonicosahexacosihecatonicosachoron (**ghixhi**)
* 266. Great retrohexacosidishecatonicosachoron (**girxady**)
* 267. Great dishecatonicosachoron (**gidahi**)
* 268. Great hexacosihecatonicosaintercepted hexacosihecatonicosachoron (**gixhinxhi**)
* 269. Hecatonicosaintercepted hexacosidishecatonicosachoron (**hinxady**)

### Small sphenoverted trishecatonicosachoron regiment (270-276)

* 270. Small sphenoverted trishecatonicosachoron (**swavathi**)
* 271. Great retrosphenoverted ditrigonal trishecatonicosachoron (**grawv ditathi**)
* 272. Great hecatonicosadishecatonicosachoron (**ghidy**)
* 273. Great retrotrishecatonicosachoron (**girthi**)
* 274. Great small dishecatonicosachoron (**gisady**)
* 275. Grand dishecatonicosaintercepted dishecatonicosachoron (**gad hinady**)
* 276. Hecatonicosaintercepted ditrigonal trishecatonicosachoron (**hind tathi**)

### Sphenoverted trishecatonicosachoron regiment (277-283)

* 277. Sphenoverted trishecatonicosachoron (**wavathi**)
* 278. Quasirhombated great stellated hecatonicosachoron (**qragishi**)
* 279. Great rhombic hecatonicosahecatonicosachoron (**girhihy**)
* 280. Pseudorhombic hecatonicosahecatonicosachoron (**pirhihy**)
* 281. Grand quasirhombic hecatonicosahecatonicosachoron (**gaqrahihy**)
* 282. Small prismatohecatonicosaintercepted dishecatonicosachoron (**sophinady**)
* 283. Great hecatonicosaintercepted trishecatonicosachoron (**ghinathi**)

### Great sphenoverted hexacosidishecatonicosachoron regiment (284-290)

* 284. Great sphenoverted hexacosidishecatonicosachoron (**gwavixady**)
* 285. Quasirhombated great grand stellated hecatonicosachoron (**qrigogishi**)
* 286. Great rhombic dishecatonicosachoron (**girdhi**)
* 287. Great pseudorhombic prismatohecatonicosachoron (**gipriphi**)
* 288. Grand quasirhombic prismatohecatonicosachoron (**gaqriphi**)
* 289. … (**dapinxhi**)
* 290. Prismatohecatonicosaintercepted hexacosihecatonicosachoron (**pinxady**)

### Great sphenoverted trishecatonicosachoron regiment (291-297)

* 291. Great sphenoverted trishecatonicosachoron (**gwavathi**)
* 292. Quasirhombated great facetted hexacosichoron (**qrigfix**)
* 293. Rhombic great hecatonicosahecatonicosachoron (**raghihy**)
* 294. Great pseudorhombic hecatonicosahecatonicosachoron (**gaprahihy**)
* 295. Grand quasirhombic dishecatonicosachoron (**gaqrady**)
* 296. Great prismato hecatonicosaintercepted dishecatonichoron (**gophinady**)
* 297. Grand hecatonicosaintercepted trishecatonicosachoron (**gahinathi**)

## Category 7: Bitruncates (298-306)

### Convex bitruncates (298-301)

* 298. Decachoron (**deca**)
* 299. Tesseractihexadecachoron (**tah**)
* 300. Tetracontoctachoron (**cont**, Octagonny)
* 301. Hexacosihecatonicosachoron (**xhi**)

### Starry bitruncates (302-304)

* 302. Small hecatonicosihecatonicosachoron (**shihi**)
* 303. Dishecatonicosachoron (**dahi**)
* 304. Great hexacosihecatonicosachoron (**gixhi**)

### Biquasitruncates (305-306)

* 305. Great tetracontoctachoron (**gic**, Octagrammy)
* 306. Great hecatonicosihecatonicosachoron (**ghihi**)

## Category 8: Grombates (307-329)

### Convex Great Rhombates (307-311)

* 307. Cantitruncated pentachoron (**grip**)
* 308. Cantitruncated tesseract (**grit**)
* 309. Cantitruncated icositetrachoron (**grico**)
* 310. Cantitruncated hecatonicosachoron (**grahi**)
* 311. Cantitruncated hexacosichoron (**grix**)

### Starry Great Rhombates (312-314)

* 312. Cantitruncated faceted hexacosichoron (**girfix**)
* 313. Cantitruncated grand hecatonicosachoron (**graghi**)
* 314. Cantitruncated grand hexacosichoron (**graggix**)

### Great Quasirhombates (315-321)

* 315. Quasicantitruncated tesseract (**gaqrit**)
* 316. Quasicantitruncated icositetrachoron (**gaqri**)
* 317. Quasicantitruncated great grand hecatonicosachoron (**gaqrigaghi**)
* 318. Quasicantitruncated great faceted hexacosichoron (**gaqrigafix**)
* 319. Quasicantitruncated small stellated hecatonicosachoron (**gaqrisashi**)
* 320. Quasicantitruncated great grand stellated hecatonicosachoron (**gaqrigagishi**)
* 321. Quasicantitruncated great stellated hecatonicosachoron (**gaqrigashi**)

### Cotcoics (322-329)

* 322. Tesseractihexadecatruncated tesseractihexadecachoron (**thatoth**)
* 323. tesseractihexadecaquasitruncated tesseractihexadecachoron (**thaquitoth**)
* 324. Icositetraquasitruncated tetracontoctachoron (**iquatoc**)
* 325. Hecatonicosahexacositruncated hecatonicosahexacosichoron (**hixthix**)
* 326. Dishecatonicosatruncated dishecatonicosachoron (**dahitady**)
* 327. Hecatonicosahecatonicosaquasitruncated dishecatonicosachoron (**hihiquatady**)
* 328. Dishecatonicosaquasitruncated dishecatonicosachoron (**dahiquatady**)
* 329. Hecatonicosahexacosiquasitruncated hecatonicosahexacosichoron (**hixquathix**)

## Category 9: Omnitruncates (330-351)

### Convex Omnitruncates (330-333)

* 330. Great prismatodecachoron (**gippix**, Omnitruncated pentachoron)
* 331. Great disprismatotesseractihexadecachoron (**gidpith**, Omnitruncated tesseract)
* 332. Great prismatotetracontoctachoron (**gippic**, Omnitruncated icositetrachoron)
* 333. Great disprismatohexacosahecatonicosachoron (**gidpixhi**, Omnitruncated hecatonicosachoron)

### Great Quasiprismates (334-339)

* 334. Great quasidisprismatotesseractihexadecachoron (**gaquidpoth**)
* 335. Great quasiprismatotetracontoctachoron (**gaquapac**)
* 336. Grand quasidisprismatodishecatonicosachoron (**gaquidipdy**)
* 337. Great quasidisprismatodishecatonicosachoron (**goquidipdy**)
* 338. Great quasidisprismatohecatonicosihecatonicosachoron (**gaquidphihi**)
* 339. Great quasidisprismatohexacosahecatonicosachoron (**gaquidapixhi**)

### Cotcoics (340-347)

* 340. Tesseractihexadecatruncated prismatotesseractihexadecachoron (**thatpath**)
* 341. Tesseractihexadecaquasitruncated prismatotesseractihexadecachoron (**thaquitpath**)
* 342. Icositetraquasitruncated prismatotetracontoctachoron (**iquatpic**)
* 343. Hecatonicosihexacosatruncated prismatohecatonicosahexacosachoron (**hixtaphix**)
* 344. Dishecatonicosatruncated prismatodishecatonicosachoron (**dohitipady**)
* 345. Hecatonicosahexacosaquasitruncated prismatohecatonicosahexacosachoron (**hixquaiphix**)
* 346. Small dishecatonicosaquasitruncated prismatodishecatonicosachoron (**sidhiquit paddy**)
* 347. Great dishecatonicosaquasitruncated prismatodishecatonicosachoron (**gidhiquit paddy**)

### Others (348-351)

* 348. Distetracontoctachoron (**doc**)
* 349. Tetracontoctarhombated tetracontoctachoron (**croc**)
* 350. Tetracontoctaquasirhombated tetracontoctachoron (**coqroc**)
* 351. Hexacosatrishecatonicosachoron (**xithi**)

## Category 10: Prismatorhombates (352-441)

### Convex Prismatorhombates (352-369)

#### Prismatorhombated pentachoron regiment (352-354)

* 352. Prismatorhombated pentachoron (**prip**, Cantellated pentachoron)
* 353. Prismatotrispentachoron (**pittip**)
* 354. Rhombiprismic dispentachoron (**ripdip**)

#### Prismatorhombated tesseract regiment (355-357)

* 355. Prismatorhombated tesseract (**prit**, Cantitruncated tesseract)
* 356. Small cubihexadecadisoctachoron (**sichado**)
* 357. Small rhombiprismic disoctachoron (**sirpdo**)

#### Prismatorhombated tesseract regiment (358-360)

* 358. Prismatorhombated tesseract (**proh**, Cantitruncated tesseract)
* 359. Small prismatohexadecadisoctachoron (**siphado**)
* 360. Small rhombiprismic tesseractitesseract (**sirpith**)

#### Prismatorhombated icositetrachoron regiment (361-363)

* 361. Prismatorhombated icositetrachoron (**prico**, Cantitruncated icositetrachoron)
* 362. Small prismatotrisicositetrachoron (**sipti**)
* 363. Small rhombiprismic disicositetrachoron (**sirpdi**)

#### Prismatorhombated hecatonicosachoron regiment (364-366)

* 364. Prismatorhombated hecatonicosachoron (**prahi**, Cantitruncated hexacontachoron)
* 365. Small prismatohexacontadishecatonicosachoron (**spixady**)
* 366. Small rhombiprismic dishecatonicosachoron (**sripady**)

#### Prismatorhombated hexacontachoron (367-369)

* 367. Prismatorhombated hexacontachoron (**prix**, Cantitruncated hecatonicosachoron)
* 368. Small prismatohexacontahecatonicosahecatonicosachoron (**spixhihy**)
* 369. Small rhombiprismic hexacontahecatonicosachoron (**sirpaxhi**)

### Starry Prismatorhombates (370-378)

#### Prismatorhombated stellated hexacosichoron regiment (370-372)

* 370. Prismatorhombated stellated hexacontachoron (**pirshi**)
* 371. Small prismatohecatonicosahecatonicosahexacosichoron (**sphihix**)
* 372. Small rhombiprismatohecatonicosahexacosichoron (**sriphix**)

#### Prismatorhombated great hecatonicosachoron regiment (373-375)

* 373. Prismatorhombated great hecatonicosachoron (**pirghi**)
* 374. Small prismatohecatonicosahecatonicosahexacosichoron (**sphihix**)
* 375. Small rhombiprismatohecatonicosahexacosichoron (**sriphix**)

#### Prismatorhombated great grand hecatonicosachoron regiment (376-378)

* 376. Prismatorhombated great hecatonicosachoron (**pirghi**)
* 377. Small prismatohecatonicosadishecatonicosachoron (**siphidy**)
* 378. Small rhombiprismic hecatonicosahecatonicosachoron (**sirphihy**)

### Quasiprismatorhombates (379-393)

#### Quasiprismatorhombated hexadecachoron regiment (379-381)

* 379. Quasiprismatorhombated hexadecachoron (**quiproh**)
* 380. Great prismatohexadecadisoctachoron (**giphado**)
* 381. Great rhombiprismic tesseractihexadecachoron (**girpith**)

#### Quasiprismatorhombated faceted hexacosichoron regiment (382-384)

* 382. Quasiprismatorhombated faceted hexacosichoron (**quippirfix**)
* 383. Great prismatotrishecatonicosachoron (**gipthi**)
* 384. Rhombiprismic dishecatonicosachoron (**rappady**)

#### Quasiprismatothombated grand stellated hecatonicosachoron regiment (385-387)

* 385. Quasiprismatorhombated grand stellated hecatonicosachoron (**quippirgashi**)
* 386. Great prismatohecatonicosadishecatonicosachoron (**giphidy**)
* 387. Great rhombiprismic hecatonicosahecatonicosachoron (**girphihy**)

#### Quasiprismatorhombated grand hecatonicosachoron regiment (388-390)

* 388. Quasiprismatorhombated grand hecatonicosachoron (**quippirghi**)
* 389. Grand prismatotrishecatonicosachoron (**gapthi**)
* 390. Rhombiprismic hecatonicosahecatonicosachoron (**raphihy**)

#### Quasiprismatorhombated grand hexacontachoron regiment (391-393)

* 391. Quasiprismatorhombated grand hexacosichoron (**quippirgax**)
* 392. Great prismatohexacosihecatonicosahecatonicosachoron (**gippixhihy**)
* 393. Great rhombiprismic hexacosihecatonicosachoron (**girpixhi**)

### Prismatoquasirhombates (394-408)

#### Great cubihexadecadisoctachoron regiment (394-396)

* 394. Great cubihexadecadisoctachoron (**gichado**)
* 395. Prismatoquasirhombated tesseract (**paqrit**)
* 396. Great rhombiprismic disoctachoron (**girpdo**)

#### Great prismatotrisicositetrachoron regiment (397-399)

* 397. Great prismatotrisicositetrachoron (**gipti**)
* 398. Prismatoquasirhombated icositetrachoron (**paqri**)
* 399. Great rhombiprismic disicositetrachoron (**girpdi**)

#### Medial prismatotrishecatonicosachoron regiment (400-402)

* 400. Medial prismatotrishecatonicosachoron (**mipthi**)
* 401. Prismatoquasirhombated great stellated hecatonicosachoron (**paqrigshi**)
* 402. Medial rhombiprismic hecatonicosahecatonicosachoron (**marphihy**)

#### Small prismatotrishecatonicosachoron regiment (403-405)

* 403. Small prismatotrishecatonicosachoron (**sipthi**)
* 404. Prismatoquasirhombated great faceted hexacosichoron (**paqrigafix**)
* 405. Medial rhombiprismic dishecatonicosachoron (**mirpady**)

#### Great prismatohexacontadishecatonicosachoron regiment (406-408)

* 406. Great prismatohexacosidishecatonicosachoron (**gippixady**)
* 407. Prismatoquasirhombated great grand stellated hecatonicosachoron (**paqrigagishi**)
* 408. Great rhombiprismic dishecatonicosachoron (**gripady**)

### Cotcoics (409-423)

#### Small tetrisicositetrachoron regiment (409-411)

* 409. Small tetrisicositetrachoron (**suti**)
* 410. Disicositetraquasitruncated disicositetrachoron (**diquitdi**)
* 411. Small rhombic trisicositetrachoron (**sirti**)

#### Disicositetratruncated disicositetrachoron regiment (412-414)

* 412. Disicositetratruncated disicositetrachoron (**ditdi**)
* 413. Great tetrisicositetrachoron (**guti**)
* 414. Great rhombic trisicositetrachoron (**girti**)

#### Hecatonicosahexacontatruncated hexacontahecatonicosachoron regiment (415-417)

* 415. Hecatonicosihexacontatruncated hexacontahecatonicosachoron (**hixtixhi**)
* 416. Great hexacontatrishecatonicosachoron (**gixathi**)
* 417. Great rhombic trishexatonicosachoron (**grithi**)

#### Hecatonicosahexacontadishecatonicosachoron regiment (418-420)

* 418. Hecatonicosahexacontadishecatonicosachoron (**hixady**)
* 419. Hexacontahecatonicosidishecatonicosachoron (**xhidy**)
* 420. Rhombic hexacontadishecatonicosachoron (**rixady**)

#### Small hexacontatrishecatonicosachoron regiment (421-423)

* 421. Small hexacontatrishecatonicosachoron (**sixathi**)
* 422. Hecatonicosihexacontaquasitruncated hexacontahecatonicosachoron (**hixquitixhi**)
* 423. Small rhombic trishecatonicosachoron (**srithi**)

## Category 16: Antifrustic hexacositrishecatonicosachoron regiment (665-763)

* 709. Great sphenoretrofrustary trishecatonicosachoron (**gwirfthi**)

## Category 17: Small stellated hecatonicosachoron regiment (764-777)

* 768. Pentagram prismatic heptacosicosachoron (**paphicki**, small prismosaurus)
* 769. Pentagon prismatic heptacosicosachoron (**paphacki**, great prismosaurus)

## Category 19: Prisms (2, 889-962)

### Regular polyhedral prisms (2, 889-896)

* 2. **Tesseract** (**tes**)
* 889. Tetrahedral prism (**tepe**)
* 890. Octahedral prism (**ope**)
* 891. Dodecahedral prism (**dope**)
* 892. Icosahedral prism (**ipe**)
* 893. Great dodecahedral prism (**gaddip**)
* 894. Small stellated dodecahedral prism (**sissiddip**)
* 895. Great icosahedral prism (**gipe**)
* 896. Great stellated dodecahedral prism (**gissiddip**)

### Truncated polyhedral prisms (898-907)

* 898. Truncated tetrahedral prism (**tuttip**)
* 899. Truncated cubic prism (**ticcup**)
* 900. Truncated octahedral prism (**tope**)
* 901. Truncated dodecahedral prism (**tiddip**)
* 902. Truncated icosahedral prism (**tipe**)
* 903. Truncated great dodecahedral prism (**tigiddip**)
* 904. Truncated great icosahedral prism (**tiggipe**)
* 905. Quasitruncated hexahedral prism (**quithip**)
* 906. Quasitruncated small stellated dodecahedral prism (**quit sissiddip**)
* 907. Quasitruncated great stellated dodecahedral prism (**quit gissiddip**)

### Quasiregular polyhedral prisms (897, 908-922)

* 897. Tetrahemihexahedral prism (**thahp**)
* 908. Cuboctahedral prism (**cope**)
* 909. Octahemioctahedral prism (**ohope**)
* 910. Cubohemioctahedral prism (**chope**)
* 911. Icosidodecahedral prism (**iddip**)
* 912. Small dodecahemidodecahedral prism (**sidhiddip**)
* 913. Small icosihemidodecahedral prism (**seihiddip**)
* 914. Dodecadodecahedral prism (**diddip**)
* 915. Small dodecahemicosahedral prism (**sidhipe**)
* 916. Great dodecahemicosahedral prism (**gidhipe**)
* 917. Great icosidodecahedral prism (**giddip**)
* 918. Great dodecahemidodecahedral prism (**gidhiddip**)
* 919. Great icosihemidodecahedral prism (**geihiddip**)
* 920. Small ditrigonary icosidodecahedral prism (**sidtiddip**)
* 921. Ditrigonary dodecadodecahedral prism (**ditdiddip**)
* 922. Great ditrigonary icosidodecahedral prism (**gidtiddip**)

### Trapezivert polyhedral prisms (923-943)

* 923. Small rhombicuboctahedral prism (**sircope**)
* 924. Small cubicuboctahedral prism (**soccope**)
* 925. Small rhombihexahedral prism (**srohp**)
* 926. Rhombicosidodecahedral prism (**sriddip**)
* 927. Small dodekicosidodecahedral prism (**saddiddip**)
* 928. Small rhombidodecahedral prism (**sirdip**)
* 929. Rhombidodecadodecahedral prism (**radiddip**)
* 930. Icosidodecadodecahedral prism (**ididdip**)
* 931. Rhombicosahedral prism (**ripe**)
* 932. Great cubicuboctahedral prism (**goccope**)
* 933. Great rhombicuboctahedral prism (**quercope**)
* 934. Great rhombihexahedral prism (**grohp**)
* 935. Great ditrigonary dodekicosidodecahedral prism (**gidditdiddip**)
* 936. Great icosicosidodecahedral prism (**giidip**)
* 937. Great dodekicosahedral prism (**giddipe**)
* 938. Great dodekicosidodecahedral prism (**gaddiddip**)
* 939. Great rhombicosidodecahedral prism (**qriddip**)
* 940. Great rhombidodecahedral prism (**girdip**)
* 941. Small icosicosidodecahedral prism (**siidip**)
* 942. Small ditrigonary dodekicosidodecahedral prism (**sidditdiddip**)
* 943. Small dodekicosahedral prism (**siddipe**)

### Omnitruncated polyhedral prisms (944-950)

* 944. Great rhombicuboctahedral prism (**gircope**)
* 945. Great icosidodecahedral prism (**griddip**)
* 946. Quasitruncated cuboctahedral prism (**quitcope**)
* 947. Quasitruncated dodecadodecahedral prism (**quitdiddip**)
* 948. Great quasitruncated icosidodecahedral prism (**gaquatiddip**)
* 949. Cuboctitruncated cuboctahedral prism (**cotcope**)
* 950. Icosidodecatruncated icosidodecahedral prism (**idtiddip**)

### Snub polyhedral prisms (951-962)

* 951. Snub cubic prism (**sniccup**)
* 952. Snub dodecahedral prism (**sniddip**)
* 953. Snub dodecadodecahedral prism (**siddiddip**)
* 954. Great snub icosidodecahedral prism (**gosiddip**)
* 955. Small snub icosicosidodecahedral prism (**sesidip**)
* 956. Inverted snub dodecadodecahedral prism (**isdiddip**)
* 957. Great inverted snub icosidodecahedral prism (**gisiddip**)
* 958. Snub icosidodecadodecahedral prism (**sididdip**)
* 959. Great snub dodekicosidodecahedral prism (**gisdiddip**)
* 960. Great inverted retrosnub icosidodecahedral prism (**girsiddip**)
* 961. Small inverted retrosnub icosicosidodecahedral prism (**sirsiddip**)
* 962. Great dirhombicosidodecahedral prism (**gidriddip**)

## Category 20: Miscellaneous (962-984, 1846-1855)

### Antiprisms (963-968, 1854-1855)

* 963. Grand antiprism (**gap**)
* 964. Pentagrammattic double antiprismoid (**padiap**)
* 965. Great duoantiprism (**gudap**)
* 966. Small ditrigonary icosidodecahedral antiprism (**sidtidap**)
* 967. Ditrigonary dodecadodecahedral antiprism (**ditdidap**)
* 968. Great ditrigonary icosidodecahedral antiprism (**gidtidap**)
* 1854. Pentacubic extended duofacetoantiprism (**pecuexidfap**)
* 1855. Pentacubic extended duoantiprism (**pecuexdap**)

### Snubs (969-974)

* 969. Snub disicositetrachoron (**sadi**)
* 970. Retrosnub disicositetrachoron (**rasdi**)
* 971. Retroantiprismatosnub disicositetrachoron (**rappisdi**)
* 972. Small retrohemiantiprismatosnub prismatodisicositetrachoron (**sirhapsippady**)
* 973. Great retrohemiantiprismatosnub prismatodisicositetrachoron (**girhapsippady**)
* 974. Retroantiprismatosnub dishecatonicosachoron (**rapsady**)

### Swirlprisms (975-982, 1850-1851)

* 975. Small swirlprism (**sisp**)
* 976. Great swirlprism (**gisp**)
* 977. Swirlprismattic hecatonicosahexacosichoron (**sphix**)

### Ondip, gondip, ixitic (1846-1849, 1852-1853)

* 1849. Great ditetragonal spinoduoprism (**gidtindip**)

## Category 22: Great dipentary trishecatonicosachoron regiment (1066-1146)

* 1138. Great dipentary trishecatonicosadishecatonicosachoron (**gidpathidy**)

## Category 23: Rectified small ditrigonal hexacosihecatonicosachoron regiment (1147-1303)

* 1285. Great ditrigonary hexacositetrishecatonicosahexacosichoron (**gidtuxthix**)

## Category 28: Small snubs (1492-1668)

* 1581. Small dispinosnub snub prismatosnub pentishecatonicosatetrishexacosichoron (**sidansos posphitux**, Darth Vader)

## Category 29: Great snubs (1669-1845)

* 1695. Great disnub snub hexishexacosipentishecatonicosachoron (**gidsoshaxphi**)

## Category A: Duoprisms

There are an infinite number of duoprisms; one for each unordered pair of polygons. Some of these are:

* {3,3} - Trigonal duoprism (**triddip**)
* {3,4} - Trigonal-square duoprism (**tisdip**)
* {3,5} - Trigonal-pentagonal duoprism (**trapedip**)
* {3,6} - Trigonal-hexagonal duoprism (**thiddip**)
* [...]
* {4,4} - Tesseract (**tes**)
* {4,5} - Square-pentagonal duoprism (**squipdip**)
* {4,6} - Square-hexagonal duoprism (**shiddip**)
* [...]
* {5,5} - Pentagonal duoprism (**pedip**)
* {5,6} - Pentagonal-hexagonal duoprism (**phiddip**)
* [...]
* {6,6} - Hexagonal duoprism (**hiddip**)
* [...]
* [...]