Table of polyhedron dihedral angles

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The dihedral angles for the edge-transitive polyhedra are:

Picture Name Schläfli
exact dihedral angle
dihedral angle
– exact in bold,
else approximate
Platonic solids (regular convex)
Tetrahedron.png Tetrahedron {3,3} (3.3.3) arccos(1/3) 70.53°
Hexahedron.png Hexahedron or Cube {4,3} (4.4.4) π/2 90°
Octahedron.png Octahedron {3,4} ( π − arccos(1/3) 109.47°
Dodecahedron.png Dodecahedron {5,3} (5.5.5) π − arctan(2) 116.56°
Icosahedron.png Icosahedron {3,5} ( π − arccos(5/3) 138.19°
Kepler–Poinsot solids (regular nonconvex)
Small stellated dodecahedron.png Small stellated dodecahedron {5/2,5} (5/2.5/2.5/2.5/2.5/2) π − arctan(2) 116.56°
Great dodecahedron.png Great dodecahedron {5,5/2} ( arctan(2) 63.435°
Great stellated dodecahedron.png Great stellated dodecahedron {5/2,3} (5/2.5/2.5/2) arctan(2) 63.435°
Great icosahedron.png Great icosahedron {3,5/2} ( arcsin(2/3) 41.810°
Quasiregular polyhedra (Rectified regular)
Uniform polyhedron-33-t1.png Tetratetrahedron r{3,3} ( π − arccos(1/3) 109.47°
Cuboctahedron.png Cuboctahedron r{3,4} ( π − arccos(1/3) 125.264°
Icosidodecahedron.png Icosidodecahedron r{3,5} ( 142.623°
Dodecadodecahedron.png Dodecadodecahedron r{5/2,5} (5.5/2.5.5/2) π − arctan(2) 116.56°
Great icosidodecahedron.png Great icosidodecahedron r{5/2,3} (3.5/2.3.5/2) 37.377°
Ditrigonal polyhedra
Small ditrigonal icosidodecahedron.png Small ditrigonal icosidodecahedron a{5,3} (3.5/2.3.5/2.3.5/2)
Ditrigonal dodecadodecahedron.png Ditrigonal dodecadodecahedron b{5,5/2} (5.5/3.5.5/3.5.5/3)
Great ditrigonal icosidodecahedron.png Great ditrigonal icosidodecahedron c{3,5/2} (
Tetrahemihexahedron.png Tetrahemihexahedron o{3,3} (3.4.3/2.4) 54.73°
Cubohemioctahedron.png Cubohemioctahedron o{3,4} (4.6.4/3.6) 54.73°
Octahemioctahedron.png Octahemioctahedron o{4,3} (3.6.3/2.6) 70.53°
Small dodecahemidodecahedron.png Small dodecahemidodecahedron o{3,5} (5.10.5/4.10) 26.063°
Small icosihemidodecahedron.png Small icosihemidodecahedron o{5,3} (3.10.3/2.10) 116.56°
Great dodecahemicosahedron.png Great dodecahemicosahedron o{5/2,5} (5.6.5/4.6)
Small dodecahemicosahedron.png Small dodecahemicosahedron o{5,5/2} (5/2.6.5/3.6)
Great icosihemidodecahedron.png Great icosihemidodecahedron o{5/2,3} (3.10/3.3/2.10/3)
Great dodecahemidodecahedron.png Great dodecahemidodecahedron o{3,5/2} (5/2.10/3.5/3.10/3)
Quasiregular dual solids
Hexahedron.png Rhombic hexahedron
(Dual of tetratetrahedron)
V( ππ/2 90°
Rhombic dodecahedron.png Rhombic dodecahedron
(Dual of cuboctahedron)
V( ππ/3 120°
Rhombic triacontahedron.png Rhombic triacontahedron
(Dual of icosidodecahedron)
V( ππ/5 144°
DU36 medial rhombic triacontahedron.png Medial rhombic triacontahedron
(Dual of dodecadodecahedron)
V(5.5/2.5.5/2) ππ/3 120°
DU54 great rhombic triacontahedron.png Great rhombic triacontahedron
(Dual of great icosidodecahedron)
V(3.5/2.3.5/2) π2π/5 72°
Duals of the ditrigonal polyhedra
DU30 small triambic icosahedron.png Small triambic icosahedron
(Dual of small ditrigonal icosidodecahedron)
DU41 medial triambic icosahedron.png Medial triambic icosahedron
(Dual of ditrigonal dodecadodecahedron)
DU47 great triambic icosahedron.png Great triambic icosahedron
(Dual of great ditrigonal icosidodecahedron)
Duals of the hemipolyhedra
Tetrahemihexacron.png Tetrahemihexacron
(Dual of tetrahemihexahedron)
V(3.4.3/2.4) ππ/2 90°
Hexahemioctacron.png Hexahemioctacron
(Dual of cubohemioctahedron)
V(4.6.4/3.6) ππ/3 120°
Hexahemioctacron.png Octahemioctacron
(Dual of octahemioctahedron)
V(3.6.3/2.6) ππ/3 120°
Small dodecahemidodecacron.png Small dodecahemidodecacron
(Dual of small dodecahemidodecacron)
V(5.10.5/4.10) ππ/5 144°
Small dodecahemidodecacron.png Small icosihemidodecacron
(Dual of small icosihemidodecacron)
V(3.10.3/2.10) ππ/5 144°
Small dodecahemicosacron.png Great dodecahemicosacron
(Dual of great dodecahemicosahedron)
V(5.6.5/4.6) ππ/3 120°
Small dodecahemicosacron.png Small dodecahemicosacron
(Dual of small dodecahemicosahedron)
V(5/2.6.5/3.6) ππ/3 120°
Great dodecahemidodecacron.png Great icosihemidodecacron
(Dual of great icosihemidodecacron)
V(3.10/3.3/2.10/3) π2π/5 72°
Great dodecahemidodecacron.png Great dodecahemidodecacron
(Dual of great dodecahemidodecacron)
V(5/2.10/3.5/3.10/3) π2π/5 72°


  • Coxeter, Regular Polytopes (1963), Macmillan Company
    • Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 (Table I: Regular Polytopes, (i) The nine regular polyhedra {p,q} in ordinary space)
  • Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-7 to 3-9)
  • Weisstein, Eric W. "Uniform Polyhedron". MathWorld.