| Picture |
Name |
Schläfli
symbol |
Vertex/Face
configuration |
exact dihedral angle
(radians) |
dihedral angle
– exact in bold,
else approximate
(degrees) |
| Platonic solids (regular convex) |
 |
Tetrahedron |
{3,3} |
(3.3.3) |
 |
70.529° |
 |
Hexahedron or Cube |
{4,3} |
(4.4.4) |
 |
90° |
 |
Octahedron |
{3,4} |
(3.3.3.3) |
 |
109.471° |
 |
Dodecahedron |
{5,3} |
(5.5.5) |
 |
116.565° |
 |
Icosahedron |
{3,5} |
(3.3.3.3.3) |
 |
138.190° |
| Kepler–Poinsot polyhedra (regular nonconvex) |
 |
Small stellated dodecahedron | {5/2,5} |
(5/2.5/2.5/2.5/2.5/2) |
|
116.565° |
 |
Great dodecahedron | {5,5/2} |
(5.5.5.5.5)/2 |
 |
63.435° |
 |
Great stellated dodecahedron | {5/2,3} |
(5/2.5/2.5/2) |
|
63.435° |
 |
Great icosahedron | {3,5/2} |
(3.3.3.3.3)/2 |
 |
41.810° |
| Quasiregular polyhedra (Rectified regular) |
 |
Tetratetrahedron |
r{3,3} |
(3.3.3.3) |
|
109.471° |
 |
Cuboctahedron |
r{3,4} |
(3.4.3.4) |
 |
125.264° |
 |
Icosidodecahedron |
r{3,5} |
(3.5.3.5) |
 |
142.623° |
 |
Dodecadodecahedron |
r{5/2,5} |
(5.5/2.5.5/2) |
|
116.565° |
 |
Great icosidodecahedron |
r{5/2,3} |
(3.5/2.3.5/2) |
 |
37.377° |
| Ditrigonal polyhedra |
 |
Small ditrigonal icosidodecahedron |
a{5,3} |
(3.5/2.3.5/2.3.5/2) |
|
142.623° |
 |
Ditrigonal dodecadodecahedron |
b{5,5/2} |
(5.5/3.5.5/3.5.5/3) |
|
63.435° |
 |
Great ditrigonal icosidodecahedron |
c{3,5/2} |
(3.5.3.5.3.5)/2 |
 |
79.188° |
| Hemipolyhedra |
 |
Tetrahemihexahedron |
o{3,3} |
(3.4.3/2.4) |
 |
54.736° |
 |
Cubohemioctahedron |
o{3,4} |
(4.6.4/3.6) |
|
54.736° |
 |
Octahemioctahedron |
o{4,3} |
(3.6.3/2.6) |
|
70.529° |
 |
Small dodecahemidodecahedron |
o{3,5} |
(5.10.5/4.10) |
 |
26.058° |
 |
Small icosihemidodecahedron |
o{5,3} |
(3.10.3/2.10) |
|
116.565° |
 |
Great dodecahemicosahedron |
o{5/2,5} |
(5.6.5/4.6) |
|
37.377° |
 |
Small dodecahemicosahedron |
o{5,5/2} |
(5/2.6.5/3.6) |
|
79.188° |
 |
Great icosihemidodecahedron |
o{5/2,3} |
(3.10/3.3/2.10/3) |
|
37.377° |
 |
Great dodecahemidodecahedron |
o{3,5/2} |
(5/2.10/3.5/3.10/3) |
|
63.435° |
| Quasiregular dual solids |
|
Rhombic hexahedron
(Dual of tetratetrahedron) |
— |
V(3.3.3.3) |
|
90° |
 |
Rhombic dodecahedron
(Dual of cuboctahedron) |
— |
V(3.4.3.4) |
 |
120° |
 |
Rhombic triacontahedron
(Dual of icosidodecahedron) |
— |
V(3.5.3.5) |
 |
144° |
 |
Medial rhombic triacontahedron
(Dual of dodecadodecahedron) |
— |
V(5.5/2.5.5/2) |
|
120° |
 |
Great rhombic triacontahedron
(Dual of great icosidodecahedron) |
— |
V(3.5/2.3.5/2) |
 |
72° |
| Duals of the ditrigonal polyhedra |
 |
Small triambic icosahedron
(Dual of small ditrigonal icosidodecahedron) |
— |
V(3.5/2.3.5/2.3.5/2) |
|
109.471° |
 |
Medial triambic icosahedron
(Dual of ditrigonal dodecadodecahedron) |
— |
V(5.5/3.5.5/3.5.5/3) |
|
109.471° |
 |
Great triambic icosahedron
(Dual of great ditrigonal icosidodecahedron) |
— |
V(3.5.3.5.3.5)/2 |
|
109.471° |
| Duals of the hemipolyhedra |
 |
Tetrahemihexacron
(Dual of tetrahemihexahedron) |
— |
V(3.4.3/2.4) |
 |
90° |
 |
Hexahemioctacron
(Dual of cubohemioctahedron) |
— |
V(4.6.4/3.6) |
 |
120° |
|
Octahemioctacron
(Dual of octahemioctahedron) |
— |
V(3.6.3/2.6) |
|
120° |
 |
Small dodecahemidodecacron
(Dual of small dodecahemidodecacron) |
— |
V(5.10.5/4.10) |
 |
144° |
|
Small icosihemidodecacron
(Dual of small icosihemidodecacron) |
— |
V(3.10.3/2.10) |
|
144° |
 |
Great dodecahemicosacron
(Dual of great dodecahemicosahedron) |
— |
V(5.6.5/4.6) |
|
120° |
|
Small dodecahemicosacron
(Dual of small dodecahemicosahedron) |
— |
V(5/2.6.5/3.6) |
|
120° |
 |
Great icosihemidodecacron
(Dual of great icosihemidodecacron) |
— |
V(3.10/3.3/2.10/3) |
 |
72° |
|
Great dodecahemidodecacron
(Dual of great dodecahemidodecacron) |
— |
V(5/2.10/3.5/3.10/3) |
|
72° |
, 
...
