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

Cantellation, also known as (polyhedron) expansion (Stott 1910, not to be confused with general geometric expansion) is the process of radially displacing the edges or faces ...

Using either the fully supported or Miller's rules criterion (Webb), the octahedron has two reflexible stellations: the octahedron itself and the stella octangula.

Miller's rules, originally devised to restrict the number of icosahedron stellations to avoid, for example, the occurrence of models that appear identical but have different ...

A quasiregular polyhedron is the solid region interior to two dual regular polyhedra with Schläfli symbols {p,q} and {q,p}. Quasiregular polyhedra are denoted using a ...

The term "rhombicuboctahedron" is most commonly used (e.g., Wenninger 1989, p. 27; Maeder 1997) to refer to the 26-faced Archimedean solid with faces 8{3}+18{4}. Cundy and ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The term rectification is sometimes used to refer to the determination of the length of a curve. Rectification also refers to the operation which converts the midpoints of ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

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 ...