Notes:
Note: Colour coding and bold figures on vertex descriptions are my own addition. Star polygons are shown in black, normal polygons in red, retrograde polygons in bold (black or red). Factors of 2 for vertices which wrap twice around the axis are shown in blue.
| No | Vertex | Name
............................................................. |
Abbrev. | Deltahedra and Rhombihedra |
| 2Yn | Bi-Pyramids | Triangular Bipyramid
Pentagonal Bipyramid {7/3}-Bipyramid |
||
| Masons Deltahedra | 1
2 3 4 5 |
|||
| 01 | n,4,4 | Pentagonal Prism | Pip | |
| 02 | n,3,3,3 | Pentagonal Anti-prism | Pap | |
| 03 | n/d,4,4 | Pentagrammic Prism | Stip | |
| 04 | n/d,3,3,3 | Pentagrammic Anti-Prism | Stap | |
| 05 | n/(n-d),3,3,3 | Pentagrammic Crossed Anti-Prism | Sistap | |
| 06 | 3,3,3 | Tetrahedron | Tet | Deltahedron: Augmented Tetrahedron |
| 07 | 6,6,3 | Truncated Tetrahedron | Tut | |
| 08 | 3,6,3/2,6 | Octahemioctahedron | Oho | |
| 09 | 3,4,3/2,4 | Tetrahemihexahedron | Thah | |
| 10 | 3,3,3,3 | Octahedron | Oct | Deltahedron: Augmented
Octahedron Deltahedron: Excavated Octahedron |
| 11 | 4,4,4 | Cube | Cube | Rhombihedron: Cube Rhombohedron: Rhombihexahedron Deltahedron: Augmented Cube |
| 12 | 4,3,4,3 | Cuboctahedron | Co | Rhombihedron: Rhombic
Dodecahedron
Deltahedron: Augmented Rhombic Dodecahedron |
| 13 | 6,6,4 | Truncated Octahedron | Toe | |
| 14 | 8,8,3 | Truncated Cube | Tic | |
| 15 | 4,4,4,3 | Rhombicuboctahedron | Sirco | |
| 16 | 8,6,4 | Truncated Cuboctahedron | Girco | |
| 17 | 4,3,3,3,3 | Snub Cuboctahedron | Snic | |
| 18 | 4,8,3/2,8 | Small Cubicuboctahedron | Socco | |
| 19 | 4,8/3,3,8/3 | Great Cubicuboctahedron | Gocco | |
| 20 | 4,6,4/3,6 | Cubohemioctahedron | Cho | |
| 21 | 8/3,6,8 | Cubitruncated Cuboctahedron | Cotco | |
| 22 | 4,3/2,4,4 | Great Rhombicuboctahedron | Querco | |
| 23 | 8,4,8/7,4/3 | Small Rhombicube | Sroh | |
| 24 | 8/3,8/3,3 | Stellatruncated Cube | Quith | |
| 25 | 6,4,8/3 | Great Truncated Cuboctahedron | Quitco | |
| 26 | 8/3,4,8/5,4/3 | Great Rhombicube | Groh | |
| 27 | 3,3,3,3,3 | Icosahedron | Ike | |
| 28 | 5,5,5 | Dodecahedron | Doe | |
| 29 | 5,3,5,3 | Icosidodecahedron | Id | |
| 30 | 6,6,5 | Truncated Icosahedron | Ti | |
| 31 | 10,10,3 | Truncated Dodecahedron | Tid | |
| 32 | 5,4,3,4 | Rhombicosidodecahedron (small) | Srid | |
| 33 | 10,6,4 | Truncated Icosidodecahedron | Grid | |
| 34 | 5,3,3,3,3 | Snub Icosidodecahedron | Snid | |
| 35 | 3,5/2,3,5/2,3,5/2 | Small Ditrigonal Icosidodecahedron | Sidtid | |
| 36 | 3,6,5/2,6 | Small Icosicosidodecahedron | Siid | |
| 37 | 5/2,3,3,3,3,3 | Snub Disicosidodecahedron | Seside | |
| 38 | 5,10,3/2,10 | Small Dodecicosidodecahedron | Saddid | |
| 39 | 5/2,5/2,5/2,5/2,5/2 | Small Stellated Dodecahedron | Sissid | |
| 40 | (5,5,5,5,5)/2 | Great Dodecahedron | Gad | |
| 41 | 5/2,5,5/2,5 | Dodecadodecahedron | Did | |
| 42 | 10,10,5/2 | Great Truncated Dodecahedron | Tigid | |
| 43 | 5,4,5/2,4 | Rhombidodecadodecahedron | Raded | |
| 44 | 4,10,4/3,10/9 | Small Rhombidodecahedron | Sird | |
| 45 | 5/2,3,5,3,3 | Snub Dodecadodecahedron | Siddid | |
| 46 | 5/3,5,5/3,5,5/3,5 | Ditrigonary Dodecadodecahedron | Ditdid | |
| 47 | 5,10/3,3,10/3 | Great Dodekified Icosidodecahedron | Gidditdid | |
| 48 | 3,10,5/3,10 | Small Dodekified Icosidodecahedron | Sidditdid | |
| 49 | 5,6,5/3,6 | Icosified Dodecadodecahedron | Ided | |
| 50 | 10,6,10/3 | Icositruncated Dodecadodecahedron | Itdid | |
| 51 | 5/3,3,5,3,3,3 | Snub Icosidodecadodecahedron | Sided | |
| 52 | (5,3,5,3,5,3)/2 | Great Ditrigonary Icosidodecahedron | Gidtid | |
| 53 | 5,6,3/2,6 | Great Icosified Icosidodecahedron | Giid | |
| 54 | 3,10,3/2,10 | Small Icosihemidodecahedron | Seihid | |
| 55 | 6,10,6/5,10/9 | Small Dodekicosahedron | Siddy | |
| 56 | 5,10,5/4,10 | Small Dodecahemidodecahedron | Sidhid | |
| 57 | 5/2,5/2,5/2 | Great Stellated Dodecahedron | Gissid | |
| 58 | (3,3,3,3,3)/2 | Great Icosahedron | Gike | |
| 59 | 5/2,3,5/2,3 | Great Icosidodecahedron | Gid | |
| 60 | 6,6,5/2 | Great Truncated Icosahedron | Tiggy | |
| 61 | 6,4,6/5,4/3 | Rhombicosahedron | Ri | |
| 62 | 5/2,3,3,3,3 | Great Snub Icosidodecahedron | Gosid | |
| 63 | 10/3,10/3,5 | Small Stellatruncated Dodecahedron | Quit Sissid | |
| 64 | 10,10/3,4 | Stellatruncated Dodecadodecahedron | Quitdid | |
| 65 | 5/3,3,5,3,3 | Vertisnub Dodecadodecahedron | Isdid | |
| 66 | 10/3,5/2,10/3,3 | Great Dodekicosidodecahedron | Gaddid | |
| 67 | 5/2,6,5/3,6 | Small Dodecahemicosahedron | Sidhei | |
| 68 | 10/3,6,10/7,6/5 | Great Dodekicosahedron | Giddy | |
| 69 | 5/3,3,5/2,3,3,3 | Great Snub Icosidisdodecahedron | Gisdid | |
| 70 | 6,5,6,5/4 | Great Dodecahemicosahedron | Gidhei | |
| 71 | 3,10/3,10/3 | Great Stellatruncated Dodecahedron | Quit Gissid | |
| 72 | 4,5/3,4,3 | Great Rhombicosidodecahedron | Qrid | |
| 73 | 6,10/3,4 | Stellatruncated Icosidodecahedron | Gaquatid | |
| 74 | 5/3,3,3,3,3 | Great Vertisnub Icosidodecahedron | Gisid | |
| 75 | 5/2,10/3,5/3,10/3 | Great Dodecahemidodecahedron | Gidhid | |
| 76 | 3,10/3,3/2,10/3 | Great Icosihemidodecahedron | Geihid | |
| 77 | (5/3,3,3,3,3,3)/2 | Small Retrosnub Icosicosidodecahedron | Sirsid | |
| 78 | 10/3,4,10/7,4/3 | Great Rhombidodecahedron | Gird | |
| 79 | (5/2,3,3,3,3)/2 | Great Retrosnub Icosidodecahedron | Girsid | |
| 80 | (5/2,4,3,4, 5/3,4,3/2,4)/2 | Great Disnub Disicosidisdodecahedron | Gidrid |