Amazing Math: Introduction to Platonic Solids by Tanna Sunil

Author:Tanna, Sunil [Tanna, Sunil]
Language: eng
Format: epub
Publisher: Answers 2000 Limited
Published: 2014-10-25T21:00:00+00:00

(4) Because we want a convex shape, the total number of degrees in the vertices of the polygons meeting at a junction must be less than 360°. Note: It can not be exactly 360° since this would result in a planar surface (flat surface).

(5) An equilateral triangle (3-sided regular polygon) has a 60° angles at its vertices, and so the possible combinations around a polyhedron's vertex are 3 equilateral triangles (resulting in a tetrahedron), 4 equilateral triangles (resulting in an octahedron), or 5 equilateral triangles (resulting in an icosahedron). It is not possible to have a junction of 6 equilateral triangles since this would result in a planar surface, since 6 × 60° = 360°. Likewise, it is not possible to have a junction of 7 or more equilateral triangles, because this would exceed 360°.

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