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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 ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

The associahedron is the n-dimensional generalization of the pentagon. It was discovered by Stasheff in 1963 and it is also known as the Stasheff polytope. The number of ...

In general, an icosidodecahedron is a 32-faced polyhedron. A number of such solids are illustrated above. "The" (quasiregular) icosidodecahedron is the 32-faced Archimedean ...

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. Reinhardt (1922) showed that for n odd, the regular ...

"Escher's solid" is the solid illustrated on the right pedestal in M. C. Escher's Waterfall woodcut (Bool et al. 1982, p. 323). It is obtained by augmenting a rhombic ...

The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

Let a convex cyclic polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the ...