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The triakis truncated tetrahedron is a convex space-filling polyhedron which is the shape of the Voronoi cell of carbon atoms in diamond. It can be constructed from the ...

The truncated pentakis dodecahedron is a polyhedron on 180 vertices, 270 edges, and 92 faces. Its canonical polyhedron has edges of three different lengths and faces ...

The geometric span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed ...

The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

A figurate number, also (but mostly in texts from the 1500 and 1600s) known as a figural number (Simpson and Weiner 1992, p. 587), is a number that can be represented by a ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

The Neuberg A_1-circle is the locus of the polygon vertex A_1 of a triangle on a given base A_2A_3 and with a given Brocard angle omega. From the center N_1, the base A_2A_3 ...

Given a point P, the pedal triangle of P is the triangle whose polygon vertices are the feet of the perpendiculars from P to the side lines. The pedal triangle of a triangle ...

The pentagram, also called the five-point star, pentacle, pentalpha, or pentangle, is the star polygon {5/2}. It is a pagan religious symbol that is one of the oldest symbols ...

The 24-cell is a finite regular four-dimensional polytope with Schläfli symbol {3,4,3}. It is also known as the hyperdiamond or icositetrachoron, and is composed of 24 ...