User:KittyPlays/sandbox

Toruicosahedron
In geometry a Toruicosahedron is a convex polyhedron with 20 faces, 30 edges and 11 vertices, with 2 of them connected into 1 at the center. Its euler characteristic &chi; = v + f - e = 11 + 20 - 30 = 1.

As far as known, this shape has been discovered in 2018, on february 16th, by accidentally folding in the 2 vertices inside, on a straw model of an icosahedron. The convex hull is a pentagonal antiprism.

A Toruicosahedron can be described as 10 tetrahedrons placed side by side to form a pentagon pattern.

A similar polyhedron can be constructed without the central vertex as an pentagonal antiprism with the 2 pentagons removed, and 5 crossed rectangle faces added to opposite edges. It will have 10 vertices, 25 edges, 10 triangles and 5 crossed-rectangles, with Euler characteristic of 10 + 15 - 25 = 0. It represents a portion of a elongated triangular tiling, with 3 triangles and 2 squares on each vertex.

Types:
 * Icosahedral Toruicosahedron
 * Prizmal Toruicosahedron

See also:
 * Icosahedron
 * Dodecahedron
 * Great dodecahedron