Dihedral Angle Calculator for Polyhedra



Dihedral Angle Calculator
Input vetex angles, output dihedral angles
a = o
b = o
c = o
A =
B =
C =

If three faces meet at a vertex on a polyhedron and you know the three vertex angles, then you can use formulas from spherical trigonometry to compute the angles between two adjacent faces, the dihedral angle.

In the figure below, the vertex angles are labeled a, b, and c, while the dihedral angles are labled A, B, and C. (In spherical trigonometry, the subtending angles of a solid angle correspond to a, b, and c, while the surface angles correspond to A, B, and C.)

You can use the calculator on the left to compute the dihedral angles for any degree-three vertex, for example, in a tetrahedron. Some dihedral angles of common polyhedra are given in the table below.



PolyhedronExact Dihedral AngleDihedral Angle in Degrees
P
L
A
T
O
N
I
C
Regular Tetrahedroncos-1(1/3)70.52878°
Cube90°90°
Octahedroncos-1(-1/3)109.47122°
Dodecahedroncos-1(-1/√5)116.56505°
Icosahedroncos-1(-√5/3)138.18969°
Cuboctahedroncos-1(-1/√3)125.26439°
Rhombic Dodecahedron120°120°
Rhombic Triacontahedron144°144°

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