Analysis of platonic solids using HCR’s Formula for Regular Polyhedron

There are five regular polyhedrons having congruent faces each as a regular n-polygon called

platonic solids. Let a be the edge length of corresponding regular polyhedron then all the important

parameters can be calculated as tabulated below

Where,

Regular

Polyhedron (Platonic

Solid)

Inner Radius ( )

Outer Radius ( )

Mean Radius ( )

Surface Area ( )

Volume ( )

Regular Tetrahedron

3

4

√

√

( √ ) ⁄

√

√

Regular Hexahedron

(Cube)

4

6

√

(

)

Regular Octahedron

3

8

√

√

( √ )

√

√

Regular

Dodecahedron

5

12

( √ )

√ √

√ (√ )

( ( √ )

)

(√ )

√ √

( √ )

Regular

Icosahedron

3

20

( √ )

√

√ √

( ( √ )

)

√

( √ )

Estimated & illustrated by Mr Harish Chandra Rajpoot (B Tech, Mechanical Engineering)

M.M.M. University of Technology, Gorakhpur-273010 (UP) India Dec, 2014