Table of polyhedron dihedral angles
# 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° |
