Two of these generate the cube and the octahedron; five of these generate the dodecahedron and the icosahedron.
The icosahedron, having twenty equilateral triangles as faces.
That for the tetrahedron has 12 for its order, for the cube (or octahedron) 24, and for the icosahedron (or dodecahedron) 60.
Within the earth's orbit inscribe an icosahedron: the sphere inscribed in it will be Venus's orbit.
These give the solid angles of the tetrahedron, the octahedron and the icosahedron.
Now, inscribe in the Earth an icosahedron, the circle inscribed in it will be Venus.
Then inscribe in the Earth an icosahedron; the circle described in it will be Venus.
An icosahedron is a figure comprehended under twenty equal sides.
Associated words: vicenary, vigesimal, vigesimation, icosahedron.
1560s, from Greek eikosahedron, neuter of eikosahedros, from eikosi "twenty" + -hedra "seat, base, chair, face of a geometric solid," from PIE root *sed- (1) "to sit" (see sedentary). Greek eikosi is from PIE *wikmti- "twenty," from *wi- "in half," hence "two" + (d)kmti-, from root *dekm- "ten" (see ten).