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

References

• Coxeter, Regular Polytopes (1963), Macmillan Company
  • Regular Polytopes, (3rd edition, 1973), Dover edition, Template:ISBN (Table I: Regular Polytopes, (i) The nine regular polyhedra {p,q} in ordinary space)
• Template:The Geometrical Foundation of Natural Structure (book) (Section 3-7 to 3-9)
• Template:MathWorld