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The snub cube, also called the cubus simus (Kepler 1619, Weissbach and Martini 2002) or snub cuboctahedron, is an Archimedean solid having 38 faces (32 triangular and 6 ...

Cube point picking is the three-dimensional case of hypercube point picking. The average distance from a point picked at random inside a unit cube to the center is given by ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

A figurate number of the form, CCub_n=n^3+(n-1)^3=(2n-1)(n^2-n+1). The first few are 1, 9, 35, 91, 189, 341, ... (OEIS A005898). The generating function for the centered cube ...

Given the above figure (without looking at the figure below!), determine how to disengage the two slotted cube halves without cutting, breaking, or distorting. One possible ...

A Lucas cube graph of order n is a graph that can be defined based on the n-Fibonacci cube graph by forbidding vertex strings that have a 1 both in the first and last ...

Given four points chosen at random inside a unit cube, the average volume of the tetrahedron determined by these points is given by ...

The compound of the snub cube and its dual, the pentagonal icositetrahedron. Surprisingly, the tribonacci constant t is intimately related to the metric properties of the ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...

The average number of regions into which n randomly chosen planes divide a cube is N^_(n)=1/(324)(2n+23)n(n-1)pi+n+1 (Finch 2003, p. 482). The maximum number of regions is ...