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The elongated dodecahedron, also known as the extended rhombic dodecahedron and rhombo-hexagonal dodecahedron, is a space-filling polyhedron and primary parallelohedron ...

The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...

The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning graph. It has 9 vertices, 16 edges (consisting of 3 ...

Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side ...

A skew conic, also known as a gauche conic, space conic, twisted conic, or cubical conic section, is a third-order space curve having up to three points in common with a ...

The 12-faced convex deltahedra also known as the Siamese dodecahedron, which is also Johnson solid J_(84). It is implemented in the Wolfram Language as ...

In each of the ten cases with zero or unit mass, the finite part of the scalar 3-loop tetrahedral vacuum Feynman diagram reduces to four-letter "words" that represent ...

The triakis truncated tetrahedron is a convex space-filling polyhedron which is the shape of the Voronoi cell of carbon atoms in diamond. It can be constructed from the ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...