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A cube 35-compound can be constructed as the dual of the octahedron 35-compound. It will be implemented in a future version of the Wolfram Language as ...

A toroidal polyhedron is a polyhedron with genus g>=1 (i.e., one having one or more holes). Examples of toroidal polyhedra include the Császár polyhedron and Szilassi ...

The truncated dodecadodecahedral graph is the skeleton of the truncated dodecadodecahedron, which is the only uniform polyhedron for which this is the case. It will be ...

Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

The bellows conjecture asserts that all flexible polyhedra keep a constant volume as they are flexed (Cromwell 1997). The conjecture was apparently proposed by Dennis ...

There exist polyhedra which can be plaited (braided). Examples include a plaited cube and plaited icosahedron illustrated above (Pargeter 1959, Wells 1991). In the above ...

Shephard's conjecture states that every convex polyhedron admits a self-unoverlapping unfolding (Shephard 1975). This question is still unsettled (Malkevitch), though most ...

The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...