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Given a smooth manifold M with an open cover U_i, a partition of unity subject to the cover U_i is a collection of smooth, nonnegative functions psi_i, such that the support ...

The geometric centroid of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as x^_ = ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...

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 ...