|
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 hebespenorotunda |
|
18 |
36 |
20 |
of order 6 |
|