Radius of Gyration (Rg) of the 13 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 Catalan Solids (duals of the
Archimedean 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 (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
Pentagonal Hexecontahedron
60 x 5p
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