Rg-Calculator of truncated Platonic Solids
The Radius of Gyration Rg of truncated Platonic Solids will be calculated. Truncation means all vertices are cut off reducing the edge lengths (a) of the faces from 100% (a) to 0% (a/2). By this truncations the Platonic Solids transform into Archimedean Solids which have a common edge length (a1=a2) but different faces. The following transformations can be achieved by subsequent truncations:

Tedrahedron (a) - Truncated Tetrahedron (t=a/3, a1=a2) - Octahedron (t=a/2, a1=0, a2=a/2)
Octahedron (a) - Truncated Octahedron (t=a/3, a1=a2) - Cuboctahedron (t=a/2, a1=0, a2=a/2)
Hexahedron (a) - Truncated Cube (t=a/(2+√2), a1=a2) - Cuboctahedron (t=a/2, a1=0, a2=a/√2)
Icosahedron (a) - Truncated Icosahedron (t=a/3, a1=a2) - Icosidodecahedron (t=a/2, a1=0, a2=a/2)
Dodecahedron (a) - Truncated Dodecahedron (t=a/(2+2*sin(54°)), a1=a2) - Icosidodecahedron (t=a/2, a1=0, a2=a*sin(54°))

Select the type of the Platonic Solid, enter its edge length (a) and its truncation t (0 < t < a/2) resulting in a new edge length from a1=a, a2=0 (t=0) down to a1=0 (t=a/2). Rg and volume of the original Platonic Solid and those of the truncated Solid will be calculated. Also the resulting edge lengths of the truncated solids after the truncation (a1 and a2) are given.


Tetrahedron Octahedron Hexahedron Icosahedron Dodecahedron

a (original):     t (trunc. t < a/2):

a1

a2

RG

Volume

RG (trunc.)

Volume (trunc.)

Author: M.Kriechbaum, TU-Graz (2026), e-mail: manfred.kriechbaum@tugraz.at