Rg-Calculator of Polyhedra
Selected Polyhedra can consist of up to 3 different types of faces (equilateral n-polygonal or rhombic).
Enter the type and number of the (different) n-polygonal faces, their common (equilateral) edge length (a) and either
the out-sphere(ro), mid-sphere(rm) or in-sphere(ri) radius originating in the centroid of the respective polyhedron (not of the polygon!),
extending to the centroid of the faces ri (ri > 0) or of the edges rm (rm > a/(2*tan(Pi/n)) ) or of the vertices ro (ro > a/(2*sin(Pi/n)) ), respectively.
In case of rhombic faces only the in-sphere-radius (ri) can be entered together with the ratio of the rhombic axes
(0 < rx/ry < 1). Note, that the Platonic Solids (consisting of 1 type of regular polygons) have one common ro, rm, ri for the polygon (all three values are different though),
the Archimedean Solids (consisting of 2 or 3 different types of regular polygons) have one common ro, rm but different ri for the different polygons and the
Catalan Solids (consisting of 1 type of irregular polygons) have one common ri but different ro for the polygon.
The volume, surface, perimeter (sum of edge lengths), Radius of Gyration of the solid (Rgs), of the
faces (Rgf), of the edges (Rge) and of the vertices (Rgv) will be calculated for the entered parameters and also for the same shape where the
volume is normalized to 1. Units are arbitrary.