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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 ...

A pandiagonal perfect magic cube is a perfect magic cube that remains perfect when any single orthogonal section is "restacked" cyclically so that the ordering of any set of ...

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 ...

Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

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 ...

A triacontahedron is a 30-faced polyhedron. Examples include the 14-gonal antiprism, biaugmented truncated cube (Johnson solid J_(67)), 15-gonal dipyramid, 28-gonal prism, ...

The truncated dodecadodecahedron, also called the quasitruncated dodecahedron, is the uniform polyhedron with Maeder index 59 (Maeder 1997), Wenninger index 98 (Wenninger ...

The truncated dodecahedron is the 32-faced Archimedean solid with faces 20{3}+12{10}. It is also uniform polyhedron with Maeder index 26 (Maeder 1997), Wenninger index 10 ...