Truncated Tetrahedron Calculator

Calculations at a regular truncated tetrahedron. A truncated tetrahedron is constructed by cutting off the vertices of a tetrahedron in a way, so that every edge has the same length. Its dual body is the triakis tetrahedron.
Enter one value and choose the number of decimal places. Then click Calculate.

	Edge length (a):			8 faces, 18 edges, 12 vertices Faces: 4 equilateral triangles, 4 regular hexagons
	Edge length tetrahedron (a'):
	Surface area (A):
	Volume (V):
	Circumsphere radius (rc):
	Midsphere radius (rm):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

The truncated tetrahedron is an Archimedean solid. Edge length and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

Archimedean solids are regular polyhedra. Their regularity is less than that of the Platonic solids. The five Platonic solids tetrahedron, cube, octahedron, dodecahedron and icosahedron consist of the same regular polygons. The requirement for the Archimedean solids is only that they consist of regular polygons and all corners are the same. Prisms and antiprisms are excluded, otherwise their number would be infinite. There are 13 (or 15) Archimedean solids. Most consist of two different regular polygons; for the truncated cuboctahedron, rhombicosidodecahedron and truncated icosidodecahedron there are three different polygons. There are two versions of the snub cube and the snub dodecahedron that are mirror images of each other but otherwise have the same dimensions. Hence the ambiguity in the number of Archimedean solids. These 13 or 15 are all Archimedean solids there are, no more polyhedra with these properties exist. They are sorted by the number of their sides, the truncated tetrahedron being the simplest of them. Presumably all Archimedean bodies were discovered by Archimedes of Syracuse himself.