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2023-08-30 The great ditrigonal icosidodecahedron is the uniform polyhedron with Maeder index 47 (Maeder 1997), Wenninger index 87 (Wenninger 1989), Coxeter index 58 (Coxeter ...

The great truncated cuboctahedron (Maeder 1997), also called the quasitruncated cuboctahedron (Wenninger 1989, p. 145), is the uniform polyhedron with Maeder index 20 (Maeder ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

The regular dodecahedron, often simply called "the" dodecahedron, is the Platonic solid composed of 20 polyhedron vertices, 30 polyhedron edges, and 12 pentagonal faces, ...

The small cubicuboctahedron is the uniform polyhedron with Maeder index 13 (Maeder 1997), Wenninger index 69 (Wenninger 1989), Coxeter index 38 (Coxeter et al. 1954), and ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...