Radius of Gyration (Rg) of the 13 Archimedean Solids
Enter the size of either the edge length (e) or the circumscribed sphere-radius (ro) or the surface area (A) or the volume (V), of the polyhedra and the values for e, ro, A, V and for the Radius of Gyration of the solid (Rgs), of the faces (Rgf), of the edges (Rge) and of the vertices (Rgv, which is equal to ro) of the13 Archimedean Solids, will be calculated. Units are arbitrary. Source of shape images: Wikipedia.
size:
e
ro
A
V
Shape
Archimedean Solid
V
A
e
Rg(s)
Rg(f)
Rg(e)
Rg(v)
Truncated Tetrahedron
Truncated Octahedron
Truncated Cube
Truncated Icosahedron
Truncated Dodecahedron
Cuboctahedron
Icosidodecahedron
Snub Cube
Snub Dodecahedron
Small Rhombicuboctahedron
Great Rhombicuboctahedron
Small Rhombicosidodecahedron
Great Rhombicosidodecahedron
Radius of Gyration (Rg) of the 13 Archimedean Duals (Catalan Solids)
Enter the size of either the inscribed sphere-radius (ri) or the surface area (A) or the volume (V), of the polyhedra and the values for ri, A, V and for the Radius of Gyration of the solid Rg(s) and of the the faces Rg(f) (polyhedron shell) for the 13 Duals of the Archimedean Solids (Catalan Solids) will be calculated. These consist of n x polygonal faces which can be 3p trigonal (is, isosceles or sc, scalene), 4p tetragonal (rh, rhombic or dt, deltoidal) or 5p pentagonal (ir, irregular, having 2 different edge lengths). Units are arbitrary.
size:
ri
A
V
Catalan Solid
faces
V
A
ri
Rg(s)
Rg(f)
Triakis Tetrahedron
12 x 3p(is)
Tetrakis Hexahedron
24 x 3p(is)
Triakis Octahedron
24 x 3p(is)
Pentakis Dodecahedron
60 x 3p(is)
Triakis Icosahedron
60 x 3p(is)
Rhombic Dodecahedron
12 x 4p(rh)
Rhombic Triacontahedron
30 x 4p(rh)
Pentagonal Icositetrahedron
24 x 5p(ir)
Pentagonal Hexecontahedron
60 x 5p(ir)
Deltoidal Icositetrahedron
24 x 4p(dt)
Disdyakis Dodecahedron
48 x 3p(sc)
Deltoidal Hexecontahedron
60 x 4p(dt)
Disdyakis Triacontahedron
120 x 3p(sc)
Author:
M.Kriechbaum
, TU-Graz (2025), e-mail:
manfred.kriechbaum@tugraz.at