Dodecahedron Formulas

Posted In: Mathematics

In geometry, a dodecahedron (plural: dodecahedra) is a polyhedron with twelve flat faces, twenty vertices and thirty edges. The term is most commonly used to refer to the regular dodecahedron, a Platonic solid composed of twelve equilateral pentagon.

Dodecahedron


Edge: a
Radius of inscribed circle: r
Radius of circumscribed circle: R
Surface area: S
Volume: V

  1. $r=√{10(25+11√5)}/2\ a$
  2. $R={√3(1+√5)}/4\ a$
  3. $S=3√{5(5+2√5)}\ a^2$
  4. $V=(15+7√5)/4\ a^3$

Post Tags: Geometry


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