The dihedral angles for the edge-transitive polyhedra are:
| 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) | arccos | 70.529° | |||||
| Hexahedron or Cube | (4.4.4) | arccos (0) = | 90° | |||||
| Octahedron | (3.3.3.3) | arccos (-) | 109.471° | |||||
| Dodecahedron | (5.5.5) | arccos (-) | 116.565° | |||||
| Icosahedron | (3.3.3.3.3) | arccos (-) | 138.190° | |||||
| Kepler–Poinsot solids (regular nonconvex) | ||||||||
| Small stellated dodecahedron | (....) | arccos (-) | 116.565° | |||||
| Great dodecahedron | arccos | 63.435° | ||||||
| Great stellated dodecahedron | (..) | arccos | 63.435° | |||||
| Great icosahedron | arccos | 41.810° | ||||||
| Quasiregular polyhedra (Rectified regular) | ||||||||
| Tetratetrahedron | r | (3.3.3.3) | arccos (-) | 109.471° | ||||
| Cuboctahedron | r | (3.4.3.4) | arccos (-) | 125.264° | ||||
| Icosidodecahedron | r | (3.5.3.5) | \arccos{\left(-
\sqrt{75+30\sqrt5}\right)} | 142.623° | ||||
| Dodecadodecahedron | r | (5..5.) | arccos (-) | 116.565° | ||||
| Great icosidodecahedron | r | (3..3.) | \arccos{\left(
\sqrt{75+30\sqrt5}\right)} | 37.377° | ||||
| Ditrigonal polyhedra | ||||||||
| Small ditrigonal icosidodecahedron | a | (3..3..3.) | ||||||
| Ditrigonal dodecadodecahedron | b | (5..5..5.) | ||||||
| Great ditrigonal icosidodecahedron | c | |||||||
| Hemipolyhedra | ||||||||
| Tetrahemihexahedron | o | (3.4..4) | arccos | 54.736° | ||||
| Cubohemioctahedron | o | (4.6..6) | arccos | 54.736° | ||||
| Octahemioctahedron | o | (3.6..6) | arccos | 70.529° | ||||
| Small dodecahemidodecahedron | o | (5.10..10) | \arccos{\left(
\sqrt{195-6\sqrt5}\right)} | 26.058° | ||||
| Small icosihemidodecahedron | o | (3.10..10) | arccos (-) | 116.56° | ||||
| Great dodecahemicosahedron | o | (5.6..6) | ||||||
| Small dodecahemicosahedron | o | (.6..6) | ||||||
| Great icosihemidodecahedron | o | (3...) | ||||||
| Great dodecahemidodecahedron | o | (...) | ||||||
| Quasiregular dual solids | ||||||||
| Rhombic hexahedron (Dual of tetratetrahedron) | — | V(3.3.3.3) | arccos (0) = | 90° | ||||
| Rhombic dodecahedron (Dual of cuboctahedron) | — | V(3.4.3.4) | arccos (-) = | 120° | ||||
| Rhombic triacontahedron (Dual of icosidodecahedron) | — | V(3.5.3.5) | arccos (-) = | 144° | ||||
| Medial rhombic triacontahedron (Dual of dodecadodecahedron) | — | V(5..5.) | arccos (-) = | 120° | ||||
| Great rhombic triacontahedron (Dual of great icosidodecahedron) | — | V(3..3.) | arccos = | 72° | ||||
| Duals of the ditrigonal polyhedra | ||||||||
| Small triambic icosahedron (Dual of small ditrigonal icosidodecahedron) | — | V(3..3..3.) | ||||||
| Medial triambic icosahedron (Dual of ditrigonal dodecadodecahedron) | — | V(5..5..5.) | ||||||
| Great triambic icosahedron (Dual of great ditrigonal icosidodecahedron) | — | V | ||||||
| Duals of the hemipolyhedra | ||||||||
| Tetrahemihexacron (Dual of tetrahemihexahedron) | — | V(3.4..4) | − | 90° | ||||
| Hexahemioctacron (Dual of cubohemioctahedron) | — | V(4.6..6) | − | 120° | ||||
| Octahemioctacron (Dual of octahemioctahedron) | — | V(3.6..6) | − | 120° | ||||
| Small dodecahemidodecacron (Dual of small dodecahemidodecacron) | — | V(5.10..10) | − | 144° | ||||
| Small icosihemidodecacron (Dual of small icosihemidodecacron) | — | V(3.10..10) | − | 144° | ||||
| Great dodecahemicosacron (Dual of great dodecahemicosahedron) | — | V(5.6..6) | − | 120° | ||||
| Small dodecahemicosacron (Dual of small dodecahemicosahedron) | — | V(.6..6) | − | 120° | ||||
| Great icosihemidodecacron (Dual of great icosihemidodecacron) | — | V(3...) | − | 72° | ||||
| Great dodecahemidodecacron (Dual of great dodecahemidodecacron) | — | V(...) | − | 72° |