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A space-filling polyhedron is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that ...

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

Consider a convex pentagon and extend the sides to a pentagram. Externally to the pentagon, there are five triangles. Construct the five circumcircles. Each pair of adjacent ...

The pentaflake is a fractal with 5-fold symmetry. As illustrated above, five pentagons can be arranged around an identical pentagon to form the first iteration of the ...

The (general) icosahedron is a 20-faced polyhedron (where icos- derives from the Greek word for "twenty" and -hedron comes from the Indo-European word for "seat"). Examples ...

A tetradecahedron is a 14-sided polyhedron, sometimes called a tetrakaidecahedron. Examples are illustrated above and summarized in the following table. name family augmented ...

A notation for large numbers defined by Steinhaus (1983, pp. 28-29). In this notation, denotes n^n, denotes "n in n triangles," and denotes "n in n squares." A modified ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

Home plate in the game of baseball is an irregular pentagon with two parallel sides, each perpendicular to a base. It seems reasonable to dub such a figure (i.e., a rectangle ...

Let A^' be the outermost vertex of the regular pentagon erected inwards on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...