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Give the Euler Formula and derive the three Magic Numbers!

Magic Number: 2 times as many faces as vertices








Magic Number: Average vertex valence is 6







Magic Number: 5 platonic solids
A platonic solids with Schläfli symbol

-
- All faces are
-gons:
(where
)
- All vertices have valence
:
(where
)






Number of edges cannot be negative:

Since




Gives only 5 solutions for

-
: Tetrahedron (4 triangular faces, self-dual)
-
: Octahedron (8 triangular faces, dual to Cube)
-
: Cube (6 square faces, dual to Octahedron)
-
: Icosahedron (20 triangular faces, dual to Dodecahedron)
-
: Dodecahedron (12 pentagonal faces, dual to Icosahedron)

Karteninfo:
Autor: janisborn
Oberthema: Informatik
Thema: Computergrafik
Schule / Uni: RWTH Aachen
Ort: Aachen
Veröffentlicht: 18.05.2022