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Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

A heptahedral graph is a polyhedral graph on seven nodes. There are 34 nonisomorphic heptahedral graphs, as first enumerated by Kirkman (1862-1863) and Hermes (1899ab, 1900, ...

The regular tessellation {6,3} consisting of regular hexagons (i.e., a hexagonal grid). In general, the term honeycomb is used to refer to a tessellation in n dimensions for ...

Miller's rules, originally devised to restrict the number of icosahedron stellations to avoid, for example, the occurrence of models that appear identical but have different ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...

Three-dimensional generalization of the polyominoes to n dimensions. The number of polycubes N(n) composed of n cubes are 1, 1, 2, 8, 29, 166, 1023, ... (OEIS A000162; Ball ...

There are four fully supported stellations of the rhombic dodecahedron including as usual the original solid in the count (Wells 1991; Webb). The three nontrivial ones ...

Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...

The most common statement known as Steiner's theorem (Casey 1893, p. 329) states that the Pascal lines of the hexagons 123456, 143652, and 163254 formed by interchanging the ...