Examples
The defect of any of the vertices of a regular dodecahedron (in which three regular pentagons meet at each vertex) is 36°, or π/5 radians, or 1/10 of a circle. Each of the angles is 108°; three of these meet at each vertex, so the defect is 360° − (108° + 108° + 108°) = 36°.
The same procedure can be followed for the other Platonic solids:
| Shape | Number of vertices | Polygons meeting at each vertex | Defect at each vertex | Total defect |
|---|---|---|---|---|
| tetrahedron | 4 | Three equilateral triangles | ||
| octahedron | 6 | Four equilateral triangles | ||
| cube | 8 | Three squares | ||
| icosahedron | 12 | Five equilateral triangles | ||
| dodecahedron | 20 | Three regular pentagons |
Read more about this topic: Defect (geometry)
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