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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 ...

The tetrahemihexahedron is the uniform polyhedron with Maeder index 4 (Maeder 1997), Wenninger index 67 (Wenninger 1989), Coxeter index 36 (Coxeter et al. 1954), and Har'El ...

Let G be Gauss's constant and M=1/G be its multiplicative inverse. Then M/sqrt(2)=0.8472130... (OEIS A097057) is sometimes known as the ubiquitous constant (Spanier and ...

A convex polyhedron is defined as the set of solutions to a system of linear inequalities mx<=b (i.e., a matrix inequality), where m is a real s×d matrix and b is a real ...

Take x itself to be a bracketing, then recursively define a bracketing as a sequence B=(B_1,...,B_k) where k>=2 and each B_i is a bracketing. A bracketing can be represented ...

The deltoidal icositetrahedron is the 24-faced dual polyhedron of the small rhombicuboctahedron A_6 and Wenninger dual W_(13). It is also called the trapezoidal ...