This is a list of the 75 uniform polyhedra, plus some of the infinite prism and antiprism families. They are organized by the categories on Jonathan Bowers's website. The polyhedra's corresponding Bowers acronym and vertex configuration are in parentheses and brackets respectively. Coxeter–Dynkin diagrams of the polytopes (if applicable) are also displayed.
Category 1: Regulars[]
- 1. Tetrahedron (tet) [3.3.3],
- 2. Cube (cube) [4.4.4],
- 3. Octahedron (oct) [3.3.3.3],
- 4. Dodecahedron (doe) [5.5.5],
- 5. Icosahedron (ike) [3.3.3.3.3],
- 6. Great dodecahedron (gad) [(5.5.5.5.5)/2],
- 7. Small stellated dodecahedron (sissid) [5/2.5/2.5/2.5/2.5/2],
- 8. Great icosahedron (gike) [(3.3.3.3.3)/2],
- 9. Great stellated dodecahedron (gissid) [5/2.5/2.5/2],
Category 2: Truncates[]
- 10. Truncated tetrahedron (tut) [3.6.6],
- 11. Truncated cube (tic) [3.8.8],
- 12. Truncated octahedron (toe) [4.6.6],
- 13. Truncated dodecahedron (tid) [3.10.10],
- 14. Truncated icosahedron (ti) [5.6.6],
- 15. Truncated great dodecahedron (tigid) [5/2.10.10],
- 16. Truncated great icosahedron (tiggy) [5/2.6.6],
- 17. Quasitruncated hexahedron (quith) [3.8/3.8/3],
- 18. Quasitruncated small stellated dodecahedron (quit sissid) [5.10/3.10/3],
- 19. Quasitruncated great stellated dodecahedron (quit gissid) [3.10/3.10/3],
Category 3: Quasiregulars[]
- 20. Tetrahemihexahedron (thah) [3.4.3/2.4], (2thah)
- 21. Cuboctahedron (co) [3.4.3.4],
- 22. Octahemioctahedron (oho) [3.6.3/2.6],
- 23. Cubohemioctahedron (cho) [4.6.4/3/6], (2cho)
- 24. Icosidodecahedron (id) [3.5.3.5],
- 25. Small dodecahemidodecahedron (sidhid) [5.10.5/4.10]
- 26. Small icosihemidodecahedron (seihid) [3.10.3/2.10]
- 27. Dodecadodecahedron (did) [5.5/2.5.5/2],
- 28. Small dodecahemicosahedron (sidhei) [6.5/2.6.5/3]
- 29. Great dodecahemicosahedron (gidhei) [5.6.5/4.6]
- 30. Great icosidodecahedron (gid) [3.5/2.3.5/2],
- 31. Great dodecahemidodecahedron (gidhid) [5/2.10/3.5/3.10/3]
- 32. Great icosihemidodecahedron (geihid) [3.10/3.3/2.10/3]
- 33. Small ditrigonary icosidodecahedron (sidtid) [3.5/2.3.5/2.3.5/2]
- 34. Ditrigonary dodecadodecahedron (ditdid) [5.5/3.5.5/3.5.5/3]
- 35. Great ditrigonary icosidodecahedron (gidtid) [(3.5.3.5.3.5)/2]
Category 4: Trapeziverts[]
- 36. Small rhombicuboctahedron (sirco)
- 37. Small cubicuboctahedron (socco)
- 38. Small rhombihexahedron (sroh)
- 39. Small rhombicosidodecahedron (srid)
- 40. Small dodekicosidodecahedron (saddid)
- 41. Small rhombidodecahedron (sird)
- 42. Rhombidodecadodecahedron (raded)
- 43. Icosidodecadodecahedron (ided)
- 44. Rhombicosahedron (ri)
- 45. Great cubicuboctahedron (gocco)
- 46. Great rhombicuboctahedron (querco)
- 47. Great rhombihexahedron (groh)
- 48. Great ditrigonary dodekicosidodecahedron (gidditdid)
- 49. Great icosicosidodecahedron (giid)
- 50. Great dodekicosahedron (giddy)
- 51. Small icosicosidodecahedron (siid)
- 52. Small ditrigonary dodekicosidodecahedron (sidditdid)
- 53. Small dodekicosahedron (siddy)
- 54. Great dodekicosidodecahedron (gaddid)
- 55. Great rhombicosidodecahedron (qrid)
- 56. Great rhombidodecahedron (gird)
Category 5: Omnitruncates[]
- 57. Great rhombicuboctahedron (girco)
- 58. Great icosidodecahedron (grid)
- 59. Quasitruncated cuboctahedron (quitco)
- 60. Quasitruncated dodecadodecahedron (quitdid)
- 61. Great quasitruncated icosidodecahedron (gaquatid)
- 62. Cuboctitruncated cuboctahedron (cotco)
- 63. Icosidodecatruncated icosidodecahedron (idtid)
Category 6: Snubs[]
- 64. Snub cube (snic)
- 65. Snub dodecahedron (snid)
- 66. Snub dodecadodecahedron (siddid)
- 67. Great snub icosidodecahedron (gosid)
- 68. Small snub icosicosidodecahedron (seside)
- 69. Inverted snub dodecadodecahedron (isdid)
- 70. Great inverted snub icosidodecahedron (gisid)
- 71. Snub icosidodecadodecahedron (sided)
- 72. Great snub dodekicosidodecahedron (gisdid)
- 73. Great inverted retrosnub icosidodecahedron (girsid)
- 74. Small inverted retrosnub icosicosidodecahedron (sirsid)
- 75. Great dirhombicosidodecahedron (gidrid)
Category A: Prisms[]
- Triangular prism (trip) [3.4.4],
- Pentagonal prism (pip) [5.4.4],
- Pentagrammic prism (stip) [5/2.4.4],
- Hexagonal prism (hip) [6.4.4],
- Heptagonal prism (hep) [7.4.4],
- Heptagrammic prism (ship) [7/2.4.4],
- Great heptagrammic prism (giship) [7/3.4.4],
- Octagonal prism (op) [8.4.4],
- Octagrammic prism (stop) [8/3.4.4],
- Enneagonal prism (ep) [9.4.4],
- Enneagrammic prism (step) [9/2.4.4],
- Great enneagrammic prism (gistep) [9/4.4.4],
- Decagonal prism (dip) [10.4.4],
- Decagrammic prism (stiddip) [10/3.4.4],
- ...
Category B: Antiprisms[]
- Square antiprism (squap) [4.3.3.3]
- Pentagonal antiprism (pap) [5.3.3.3]
- Pentagrammic antiprism (stap) [5/2.3.3.3]
- Pentagrammic retroprism (starp) [5/3.3.3.3]
- Hexagonal antiprism (hap) [6.3.3.3]
- Heptagonal antiprism (heap) [7.3.3.3]
- Heptagrammic antiprism (sithap) [7/2.3.3.3]
- Great heptagrammic antiprism (gisthap) [7/3.3.3.3]
- Great heptagrammic retroprism (gisthirp) [7/4.3.3.3]
- Octagonal antiprism (oap) [8.3.3.3]
- Octagrammic antiprism (stoap) [8/3.3.3.3]
- Octagrammic retroprism (storp) [8/5.3.3.3]
- Enneagonal antiprism (eap) [9.3.3.3]
- Enneagrammic antiprism (steap) [9/2.3.3.3]
- Great enneagrammic antiprism (gisteap) [9/4.3.3.3]
- Great enneagrammic retroprism (gisterp) [9/5.3.3.3]
- Decagonal antiprism (dap) [10.3.3.3]
- Decagrammic antiprism (stiddap) [10/3.3.3.3]
- ...