Topology of Surfaces

  • V. G. Boltyanskiĭ
  • V. A. Efremovich
Part of the Universitext book series (UTX)

Abstract

The table below lists the number of edges, vertices, and faces of the five Platonic solids.

The table shows that for each Platonic solid we have the relation

Name of polyhedron

Number V of vertices quotation

Number E of edges

Number F of faces

tetrahedron

4

6

4

cube

8

12

6

octahedron

6

12

8

dodecahedron

20

30

12

icosahedron

12

30

20

$$V - E + F = 2$$
(6)
It is easy to show that relation (6) is also valid for pyramids, prisms, and other polyhedra. Euler was the first to recognize and prove this important property of polyhedra.

Keywords

Singular Point Chromatic Number Euler Characteristic Intersection Index Orientable Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • V. G. Boltyanskiĭ
    • 1
  • V. A. Efremovich
  1. 1.CIMAT Guanajuato, Gto.Mexico

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