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The square gyrobicupola is a convex equilateral solid that is Johnson solid J_(29). The unit square gyrobicupola has volume V=2+4/3sqrt(2) (1) and Dehn invariant D = 24<3>_2 ...

The square orthobicupola is a convex equilateral solid that is Johnson solid J_(28). The unit square orthobicupola has volume V=2+4/3sqrt(2) (1) and Dehn invariant D = ...

There are a number of interesting results related to the tiling of squares. For example, M. Laczkovich has shown that there are exactly three shapes of non-right triangles ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...

Given a triangle with angles (pi/p, pi/q, pi/r), the resulting symmetry group is called a (p,q,r) triangle group (also known as a spherical tessellation). In three ...

The trigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating three of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...