The dihedral angles for the edge-transitive polyhedra are: Picture Name Schläflisymbol Vertex/Faceconfiguration exact dihedral angle(radians) dihedral angle– exact in bold,else approximate(degrees) Platonic solids (regular convex) Tetrahedron {3,3} (3.3.3) 70.529° 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 (....) 116.565° Great dodecahedron 63.435° Great stellated dodecahedron{,3} (..) 63.435° Great icosahedron 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} (5..5.) 116.565° Great icosidodecahedron r{,3} (3..3.) 37.377° Ditrigonal polyhedra Small ditrigonal icosidodecahedron a{5,3} (3..3..3.) 142.623° Ditrigonal dodecadodecahedron b (5..5..5.) 63.435° Great ditrigonal icosidodecahedron c 79.188° Hemipolyhedra Tetrahemihexahedron o{3,3} (3.4..4) 54.736° Cubohemioctahedron o{3,4} (4.6..6) 54.736° Octahemioctahedron o{4,3} (3.6..6) 70.529° Small dodecahemidodecahedron o{3,5} (5.10..10) 26.058° Small icosihemidodecahedron o{5,3} (3.10..10) 116.565° Great dodecahemicosahedron o{,5} (5.6..6) 37.377° Small dodecahemicosahedron o (.6..6) 79.188° Great icosihemidodecahedron o (3...) 37.377° Great dodecahemidodecahedron o (...) 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.) 120° Great rhombic triacontahedron(Dual of great icosidodecahedron) — V(3..3.) 72° Duals of the ditrigonal polyhedra Small triambic icosahedron(Dual of small ditrigonal icosidodecahedron) — V(3..3..3.) 109.471° Medial triambic icosahedron(Dual of ditrigonal dodecadodecahedron) — V(5..5..5.) 109.471° Great triambic icosahedron(Dual of great ditrigonal icosidodecahedron) — V 109.471° 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°
References Coxeter, Regular Polytopes (1963), Macmillan Company Regular Polytopes, (3rd edition, 1973), Dover edition, (Table I: Regular Polytopes, (i) The nine regular polyhedra {p,q} in ordinary space) (Section 3-7 to 3-9)