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Möbius tetrahedra, also called Möbius tetrads (Baker 1922, pp. 61-62) are a pair of tetrahedra, each of which has all the vertices lying on the faces of the other: in other ...

A multistable polyhedron is a polyhedron that can change form from one stable configuration to another with only a slight transient nondestructive elastic stretch (Goldberg ...

There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...

A first compound of 20 octahedra can be constructed from the vertices of icositruncated dodecadodecahedron uniform polyhedron and a second from the vertices of the great ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The octahemioctahedron, also called the octatetrahedron, is the uniform polyhedron with Maeder index 3 (Maeder 1997), Wenninger index 68 (Wenninger 1989), Coxeter index 37 ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

Move a point Pi_0 along a line from an initial point to a final point. It traces out a line segment Pi_1. When Pi_1 is translated from an initial position to a final ...

An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as ...