# Table of polyhedron dihedral angles

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} | (3.3.3) | arccos (⁠1/3⁠) | 70.529° |
| | Hexahedron or Cube | {4,3} | (4.4.4) | arccos (0) = ⁠π/2⁠ | 90° |
| | Octahedron | {3,4} | (3.3.3.3) | arccos (-⁠1/3⁠) | 109.471° |
| | Dodecahedron | {5,3} | (5.5.5) | arccos (-⁠√5/5⁠) | 116.565° |
| | Icosahedron | {3,5} | (3.3.3.3.3) | arccos (-⁠√5/3⁠) | 138.190° |
| Kepler–Poinsot solids (regular nonconvex) ||||||
| | Small stellated dodecahedron | {⁠5/2⁠,5} | (⁠5/2⁠.⁠5/2⁠.⁠5/2⁠.⁠5/2⁠.⁠5/2⁠) | arccos (-⁠√5/5⁠) | 116.565° |
| | Great dodecahedron | {5,⁠5/2⁠} | ⁠(5.5.5.5.5)/2⁠ | arccos (⁠√5/5⁠) | 63.435° |
| | Great stellated dodecahedron | {⁠5/2⁠,3} | (⁠5/2⁠.⁠5/2⁠.⁠5/2⁠) | arccos (⁠√5/5⁠) | 63.435° |
| | Great icosahedron | {3,⁠5/2⁠} | ⁠(3.3.3.3.3)/2⁠ | arccos (⁠√5/3⁠) | 41.810° |
| Quasiregular polyhedra (Rectified regular) ||||||
| | Tetratetrahedron | r{3,3} | (3.3.3.3) | arccos (-⁠1/3⁠) | 109.471° |
| | Cuboctahedron | r{3,4} | (3.4.3.4) | arccos (-⁠√3/3⁠) | 125.264° |
| | Icosidodecahedron | r{3,5} | (3.5.3.5) | $\arccos {\left(-{\frac {1}{15}}{\sqrt {75+30{\sqrt {5}}}}\right)}$ | 142.623° |
| | Dodecadodecahedron | r{⁠5/2⁠,5} | (5.⁠5/2⁠.5.⁠5/2⁠) | arccos (-⁠√5/5⁠) | 116.565° |
| | Great icosidodecahedron | r{⁠5/2⁠,3} | (3.⁠5/2⁠.3.⁠5/2⁠) | $\arccos {\left({\frac {1}{15}}{\sqrt {75+30{\sqrt {5}}}}\right)}$ | 37.377° |
| Ditrigonal polyhedra ||||||
| | Small ditrigonal icosidodecahedron | a{5,3} | (3.⁠5/2⁠.3.⁠5/2⁠.3.⁠5/2⁠) | | |
| | Ditrigonal dodecadodecahedron | b{5,⁠5/2⁠} | (5.⁠5/3⁠.5.⁠5/3⁠.5.⁠5/3⁠) | | |
| | Great ditrigonal icosidodecahedron | c{3,⁠5/2⁠} | ⁠(3.5.3.5.3.5)/2⁠ | | |
| Hemipolyhedra ||||||
| | Tetrahemihexahedron | o{3,3} | (3.4.⁠3/2⁠.4) | arccos (⁠√3/3⁠) | 54.736° |
| | Cubohemioctahedron | o{3,4} | (4.6.⁠4/3⁠.6) | arccos (⁠√3/3⁠) | 54.736° |
| | Octahemioctahedron | o{4,3} | (3.6.⁠3/2⁠.6) | arccos (⁠1/3⁠) | 70.529° |
| | Small dodecahemidodecahedron | o{3,5} | (5.10.⁠5/4⁠.10) | $\arccos {\left({\frac {1}{15}}{\sqrt {195-6{\sqrt {5}}}}\right)}$ | 26.058° |
| | Small icosihemidodecahedron | o{5,3} | (3.10.⁠3/2⁠.10) | arccos (-⁠√5/5⁠) | 116.56° |
| | Great dodecahemicosahedron | o{⁠5/2⁠,5} | (5.6.⁠5/4⁠.6) | | |
| | Small dodecahemicosahedron | o{5,⁠5/2⁠} | (⁠5/2⁠.6.⁠5/3⁠.6) | | |
| | Great icosihemidodecahedron | o{⁠5/2⁠,3} | (3.⁠10/3⁠.⁠3/2⁠.⁠10/3⁠) | | |
| | Great dodecahemidodecahedron | o{3,⁠5/2⁠} | (⁠5/2⁠.⁠10/3⁠.⁠5/3⁠.⁠10/3⁠) | | |
| Quasiregular dual solids ||||||
| | Rhombic hexahedron (Dual of tetratetrahedron) | — | V(3.3.3.3) | arccos (0) = ⁠π/2⁠ | 90° |
| | Rhombic dodecahedron (Dual of cuboctahedron) | — | V(3.4.3.4) | arccos (-⁠1/2⁠) = ⁠2π/3⁠ | 120° |
| | Rhombic triacontahedron (Dual of icosidodecahedron) | — | V(3.5.3.5) | arccos (-⁠√5+1/4⁠) = ⁠4π/5⁠ | 144° |
| | Medial rhombic triacontahedron (Dual of dodecadodecahedron) | — | V(5.⁠5/2⁠.5.⁠5/2⁠) | arccos (-⁠1/2⁠) = ⁠2π/3⁠ | 120° |
| | Great rhombic triacontahedron (Dual of great icosidodecahedron) | — | V(3.⁠5/2⁠.3.⁠5/2⁠) | arccos (⁠√5-1/4⁠) = ⁠2π/5⁠ | 72° |
| Duals of the ditrigonal polyhedra ||||||
| | Small triambic icosahedron (Dual of small ditrigonal icosidodecahedron) | — | V(3.⁠5/2⁠.3.⁠5/2⁠.3.⁠5/2⁠) | | |
| | Medial triambic icosahedron (Dual of ditrigonal dodecadodecahedron) | — | V(5.⁠5/3⁠.5.⁠5/3⁠.5.⁠5/3⁠) | | |
| | Great triambic icosahedron (Dual of great ditrigonal icosidodecahedron) | — | V⁠(3.5.3.5.3.5)/2⁠ | | |
| Duals of the hemipolyhedra ||||||
| | Tetrahemihexacron (Dual of tetrahemihexahedron) | — | V(3.4.⁠3/2⁠.4) | π − ⁠π/2⁠ | 90° |
| | Hexahemioctacron (Dual of cubohemioctahedron) | — | V(4.6.⁠4/3⁠.6) | π − ⁠π/3⁠ | 120° |
| | Octahemioctacron (Dual of octahemioctahedron) | — | V(3.6.⁠3/2⁠.6) | π − ⁠π/3⁠ | 120° |
| | Small dodecahemidodecacron (Dual of small dodecahemidodecacron) | — | V(5.10.⁠5/4⁠.10) | π − ⁠π/5⁠ | 144° |
| | Small icosihemidodecacron (Dual of small icosihemidodecacron) | — | V(3.10.⁠3/2⁠.10) | π − ⁠π/5⁠ | 144° |
| | Great dodecahemicosacron (Dual of great dodecahemicosahedron) | — | V(5.6.⁠5/4⁠.6) | π − ⁠π/3⁠ | 120° |
| | Small dodecahemicosacron (Dual of small dodecahemicosahedron) | — | V(⁠5/2⁠.6.⁠5/3⁠.6) | π − ⁠π/3⁠ | 120° |
| | Great icosihemidodecacron (Dual of great icosihemidodecacron) | — | V(3.⁠10/3⁠.⁠3/2⁠.⁠10/3⁠) | π − ⁠2π/5⁠ | 72° |
| | Great dodecahemidodecacron (Dual of great dodecahemidodecacron) | — | V(⁠5/2⁠.⁠10/3⁠.⁠5/3⁠.⁠10/3⁠) | π − ⁠2π/5⁠ | 72° |