| Solid name | Image | Vertices | Edges | Faces | Symmetry group and its order | Surface area and volume |
1 | Equilateral square pyramid | | 5 | 8 | 5 | of order 8 | |
2 | Pentagonal pyramid | | 6 | 10 | 6 | of order 10 | |
3 | Triangular cupola | | 9 | 15 | 8 | of order 6 | |
4 | Square cupola | | 12 | 20 | 10 | of order 8 | |
5 | Pentagonal cupola | | 15 | 25 | 12 | of order 10 | |
6 | Pentagonal rotunda | | 20 | 35 | 17 | of order 10 | |
7 | Elongated triangular pyramid | | 7 | 12 | 7 | of order 6 | |
8 | Elongated square pyramid | | 9 | 16 | 9 | of order 8 | |
9 | Elongated pentagonal pyramid | | 11 | 20 | 11 | of order 10 | |
10 | Gyroelongated square pyramid | | 9 | 20 | 13 | of order 8 | |
11 | Gyroelongated pentagonal pyramid | | 11 | 25 | 16 | of order 10 | |
12 | Triangular bipyramid | | 5 | 9 | 6 | of order 12 | |
13 | Pentagonal bipyramid | | 7 | 15 | 10 | of order 20 | |
14 | Elongated triangular bipyramid | | 8 | 15 | 9 | of order 12 | |
15 | Elongated square bipyramid | | 10 | 20 | 12 | of order 16 | |
16 | Elongated pentagonal bipyramid | | 12 | 25 | 15 | of order 20 | |
17 | Gyroelongated square bipyramid | | 10 | 24 | 16 | of order 16 | |
18 | Elongated triangular cupola | | 15 | 27 | 14 | of order 6 | |
19 | Elongated square cupola | | 20 | 36 | 18 | of order 8 | |
20 | Elongated pentagonal cupola | | 25 | 45 | 22 | of order 10 | |
21 | Elongated pentagonal rotunda | | 30 | 55 | 27 | of order 10 | |
22 | Gyroelongated triangular cupola | | 15 | 33 | 20 | of order 6 | |
23 | Gyroelongated square cupola | | 20 | 44 | 26 | of order 8 | |
24 | Gyroelongated pentagonal cupola | | 25 | 55 | 32 | of order 10 | |
25 | Gyroelongated pentagonal rotunda | | 30 | 65 | 37 | of order 10 | |
26 | Gyrobifastigium | | 8 | 14 | 8 | of order 8 | |
27 | Triangular orthobicupola | | 12 | 24 | 14 | of order 12 | |
28 | Square orthobicupola | | 16 | 32 | 18 | of order 16 | |
29 | Square gyrobicupola | | 16 | 32 | 18 | of order 16 | |
30 | Pentagonal orthobicupola | | 20 | 40 | 22 | of order 20 | |
31 | Pentagonal gyrobicupola | | 20 | 40 | 22 | of order 20 | |
32 | Pentagonal orthocupolarotunda | | 25 | 50 | 27 | of order 10 | |
33 | Pentagonal gyrocupolarotunda | | 25 | 50 | 27 | of order 10 | |
34 | Pentagonal orthobirotunda | | 30 | 60 | 32 | of order 20 | |
35 | Elongated triangular orthobicupola | | 18 | 36 | 20 | of order 12 | |
36 | Elongated triangular gyrobicupola | | 18 | 36 | 20 | of order 12 | |
37 | Elongated square gyrobicupola | | 24 | 48 | 26 | of order 16 | |
38 | Elongated pentagonal orthobicupola | | 30 | 60 | 32 | of order 20 | |
39 | Elongated pentagonal gyrobicupola | | 30 | 60 | 32 | of order 20 | |
40 | Elongated pentagonal orthocupolarotunda | | 35 | 70 | 37 | of order 10 | |
41 | Elongated pentagonal gyrocupolarotunda | | 35 | 70 | 37 | of order 10 | |
42 | Elongated pentagonal orthobirotunda | | 40 | 80 | 42 | of order 20 | |
43 | Elongated pentagonal gyrobirotunda | | 40 | 80 | 42 | of order 20 | |
44 | Gyroelongated triangular bicupola | | 18 | 42 | 26 | of order 6 | |
45 | Gyroelongated square bicupola | | 24 | 56 | 34 | of order 8 | |
46 | Gyroelongated pentagonal bicupola | | 30 | 70 | 42 | of order 10 | |
47 | Gyroelongated pentagonal cupolarotunda | | 35 | 80 | 47 | of order 5 | |
48 | Gyroelongated pentagonal birotunda | | 40 | 90 | 52 | of order 10 | |
49 | Augmented triangular prism | | 7 | 13 | 8 | of order 4 | |
50 | Biaugmented triangular prism | | 8 | 17 | 11 | of order 4 | |
51 | Triaugmented triangular prism | | 9 | 21 | 14 | of order 12 | |
52 | Augmented pentagonal prism | | 11 | 19 | 10 | of order 4 | |
53 | Biaugmented pentagonal prism | | 12 | 23 | 13 | of order 4 | |
54 | Augmented hexagonal prism | | 13 | 22 | 11 | of order 4 | |
55 | Parabiaugmented hexagonal prism | | 14 | 26 | 14 | of order 8 | |
56 | Metabiaugmented hexagonal prism | | 14 | 26 | 14 | of order 4 | |
57 | Triaugmented hexagonal prism | | 15 | 30 | 17 | of order 12 | |
58 | Augmented dodecahedron | | 21 | 35 | 16 | of order 10 | |
59 | Parabiaugmented dodecahedron | | 22 | 40 | 20 | of order 20 | |
60 | Metabiaugmented dodecahedron | | 22 | 40 | 20 | of order 4 | |
61 | Triaugmented dodecahedron | | 23 | 45 | 24 | of order 6 | |
62 | Metabidiminished icosahedron | | 10 | 20 | 12 | of order 4 | |
63 | Tridiminished icosahedron | | 9 | 15 | 8 | of order 6 | |
64 | Augmented tridiminished icosahedron | | 10 | 18 | 10 | of order 6 | |
65 | Augmented truncated tetrahedron | | 15 | 27 | 14 | of order 6 | |
66 | Augmented truncated cube | | 28 | 48 | 22 | of order 8 | |
67 | Biaugmented truncated cube | | 32 | 60 | 30 | of order 16 | |
68 | Augmented truncated dodecahedron | | 65 | 105 | 42 | of order 10 | |
69 | Parabiaugmented truncated dodecahedron | | 70 | 120 | 52 | of order 20 | |
70 | Metabiaugmented truncated dodecahedron | | 70 | 120 | 52 | of order 4 | |
71 | Triaugmented truncated dodecahedron | | 75 | 135 | 62 | of order 6 | |
72 | Gyrate rhombicosidodecahedron | | 60 | 120 | 62 | of order 10 | |
73 | Parabigyrate rhombicosidodecahedron | | 60 | 120 | 62 | of order 20 | |
74 | Metabigyrate rhombicosidodecahedron | | 60 | 120 | 62 | of order 4 | |
75 | Trigyrate rhombicosidodecahedron | | 60 | 120 | 62 | of order 6 | |
76 | Diminished rhombicosidodecahedron | | 55 | 105 | 52 | of order 10 | |
77 | Paragyrate diminished rhombicosidodecahedron | | 55 | 105 | 52 | of order 10 | |
78 | Metagyrate diminished rhombicosidodecahedron | | 55 | 105 | 52 | of order 2 | |
79 | Bigyrate diminished rhombicosidodecahedron | | 55 | 105 | 52 | of order 2 | |
80 | Parabidiminished rhombicosidodecahedron | | 50 | 90 | 42 | of order 20 | |
81 | Metabidiminished rhombicosidodecahedron | | 50 | 90 | 42 | of order 4 | |
82 | Gyrate bidiminished rhombicosidodecahedron | | 50 | 90 | 42 | of order 2 | |
83 | Tridiminished rhombicosidodecahedron | | 45 | 75 | 32 | of order 6 | |
84 | Snub disphenoid | | 8 | 18 | 12 | of order 8 | |
85 | Snub square antiprism | | 16 | 40 | 26 | of order 16 | |
86 | Sphenocorona | | 10 | 22 | 14 | of order 4 | |
87 | Augmented sphenocorona | | 11 | 26 | 17 | of order 2 | |
88 | Sphenomegacorona | | 12 | 28 | 18 | of order 4 | |
89 | Hebesphenomegacorona | | 14 | 33 | 21 | of order 4 | |
90 | Disphenocingulum | | 16 | 38 | 24 | of order 8 | |
91 | Bilunabirotunda | | 14 | 26 | 14 | of order 8 | |
92 | Triangular hebesphenorotunda | | 18 | 36 | 20 | of order 6 | |