The dihedral angle of a regular icosahedron can be calculated by adding the angle of pentagonal pyramids with regular faces and a pentagonal antiprism. The dihedral angle of a pentagonal antiprism and pentagonal pyramid between two adjacent triangular faces is approximately 38.2°. The dihedral angle of a pentagonal antiprism between pentagon-to-triangle is 100.8°, and the dihedral angle of a pentagonal pyramid between the same faces is 37.4°. Therefore, for the regular icosahedron, the dihedral angle between two adjacent triangles, on the edge where the pentagonal pyramid and pentagonal antiprism are attached is 37.4° + 100.8° = 138.2°.
The dihedral angle of a regular icosahedron can be calculated by adding the angle of pentagonal pyramids with regular faces and a pentagonal antiprism The dihedral angle of a pentagonal antiprism. and pentagonal p.yramid between two adjacent triangular faces is approximately 38.2°. The dihedral angle of a pentagonal antiprism between pentagon-to-triangle is 1008°, and the dihedral angle of a pentagonal pyramid be,tween .the same faces is 37.4°. Therefore for the regular icosahedron, the dihedral angle between two adjacent triangles, on the edge where the pentagonal pyramid and pentagonal antiprism are attached is 374° + 100.8° = 138.2°.