Editing Angular defect (section)

==Examples==

The defect of any of the vertices of a regular [[dodecahedron]] (in which three regular [[pentagon]]s meet at each vertex) is 36°, or π/5 radians, or 1/10 of a circle. Each of the angles measures 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 solid]]s:
{| class="wikitable"
!Shape
!Number of vertices 
!Polygons meeting at each vertex
!Defect at each vertex
!Total defect
|-
|[[tetrahedron]]||4||Three equilateral triangles||<math>\pi \ \ (180^\circ )</math>||<math>4\pi \ \ (720^\circ )</math>
|-
|[[octahedron]]||6||Four equilateral triangles||<math>{2 \pi\over 3} \    (120^\circ )</math>||<math>4\pi \ \ (720^\circ )</math>
|-
|[[cube]]||8||Three squares||<math>{\pi\over 2}\ \  (90^\circ )</math>||<math>4\pi \ \ (720^\circ )</math>
|-
|[[icosahedron]]||12||Five equilateral triangles||<math>{\pi\over 3}\ \  (60^\circ )</math>||<math>4\pi \ \ (720^\circ )</math>
|-
|[[dodecahedron]]||20||Three regular pentagons||<math>{\pi\over 5}\ \  (36^\circ )</math>||<math>4\pi \ \ (720^\circ )</math>
|}