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The polyhedron compound of the icosidodecahedron and its dual, the rhombic triacontahedron. The compound can be constructed from an icosidodecahedron of unit edge length by ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

A spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

A Cantor set C in R^3 is said to be scrawny if for each neighborhood U of an arbitrary point p in C, there is a neighborhood V of p such that every map f:S^1->V subset C ...

The (small) rhombicosidodecahedron (Cundy and Rowlett 1989, p. 111), sometimes simply called the rhombicosidodecahedron (Maeder 1997; Wenninger 1989, p. 27; Conway et al. ...

In general, a triakis octahedron is a non-regular icositetrahedron that can be constructed as a positive augmentation of regular octahedron. Such a solid is also known as a ...

The polyhedron compound of the truncated dodecahedron and its dual, the triakis icosahedron. The compound can be constructed from a truncated dodecahedron of unit edge length ...