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The Lemoine hexagon is a cyclic hexagon with vertices given by the six concyclic intersections of the parallels of a reference triangle through its symmedian point K. The ...

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...

The octahemioctahedron, also called the octatetrahedron, is the uniform polyhedron with Maeder index 3 (Maeder 1997), Wenninger index 68 (Wenninger 1989), Coxeter index 37 ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.

The small dodecahemicosahedron is the uniform polyhedron with Maeder index 62 (Maeder 1997), Wenninger index 100 (Wenninger 1989), Coxeter index 78 (Coxeter et al. 1954), and ...

The small icosihemidodecahedron is the uniform polyhedron with Maeder index 49 (Maeder 1997), Wenninger index 89 (Wenninger 1989), Coxeter index 63 (Coxeter et al. 1954), and ...

The small rhombidodecahedron is the uniform polyhedron with Maeder index 39 (Maeder 1997), Wenninger index 74 (Wenninger 1989), Coxeter index 46 (Coxeter et al. 1954), and ...

The small rhombihexahedron is the uniform polyhedron with Maeder index 18 (Maeder 1997), Wenninger index 86 (Wenninger 1989), Coxeter index 60 (Coxeter et al. 1954), and ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...