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A compound of five regular dodecahedra with the symmetry of the icosahedron (Wenninger 1983, pp. 145-147) can be constructed by taking a dodecahedron with top and bottom ...

The elongated pentagonal gyrobirotunda is a convex equilateral gyrobirotunda having regular pentagonal upper and lower birotundas arranged rotated 1/10 of a turn with respect ...

The elongated pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower rotundas arranged symmetrically with respect to each ...

A geometric construction, also called a verging construction, which allows the classical geometric construction rules to be bent in order to permit sliding of a marked ruler. ...

The pentagonal orthobicupola is a convex equilateral orthobicupola having regular pentagonal upper and lower faces. It is Johnson solid J_(30). The unit pentagonal ...

A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. For M in R^3, the second fundamental form is the symmetric bilinear form on the tangent ...

The Star of Lakshmi is the star figure {8/2}, that is used in Hinduism to symbolize Ashtalakshmi, the eight forms of wealth. This symbol appears prominently in the Lugash ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...