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The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

The pentakis dodecahedron is the 60-faced dual polyhedron of the truncated icosahedron A_(11) (Holden 1971, p. 55). It is Wenninger dual W_9. It can be constructed by ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

Am octagonal prims is a prism composed of octagonal faces. The regular right octagonal prism of unit edge length has surface area and volume S = 4(3+sqrt(2)) (1) V = ...

The cross polytope beta_n is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (+/-1, 0, 0, ..., 0). A ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

A convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities mx<=b, where m is a real s×3 matrix and b is a real s-vector. ...

700 The great triambic icosahedron is the dual of the great ditrigonal icosidodecahedron U_(47) and Wenninger model W_(87) whose appearance is the same as the medial triambic ...

A hexagonal prism is a prism composed of two hexagonal bases and six rectangular sides. It is an octahedron. The regular right hexagonal prism is a space-filling polyhedron. ...

1000 The medial triambic icosahedron is the dual of the ditrigonal dodecadodecahedron U_(41) and Wenninger dual W_(80), whose outward appearance is the same as the great ...