Tag Archives: dual

An Expansion of the Rhombic Enneacontahedron with 422 Faces, Together with Its 360-Faced Dual

The polyhedron above had 422 faces and 360 vertices. In dual polyhedra, these numbers are reversed, so the next polyhedra (the dual of the first one) has 360 faces and 422 vertices. Both were created using Stella 4d, available here.

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A Polyhedral Journey, Beginning With an Expansion of the Rhombic Triacontahedron

The blue figure below is the rhombic triacontahedron. It has thirty identical faces, and is one of the Catalan solids, also known as Archimedean duals. This particular Catalan solid’s dual is the icosidodecahedron. I use a program called Stella 4d … Continue reading

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The Snub Dodecahedron and Related Polyhedra, Including Compounds

The dual of the snub dodecahedron (above) is called the pentagonal hexacontahedron (below, left). The compound of the two is shown below, at right. (Any of the smaller images here may be enlarged with a click.) Like all chiral polyhedra, … Continue reading

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A Torus and Its Dual, Part II

After I published the last post, which I did not originally intend to have two parts, this comment was left by one of my blog’s followers. My answer is also shown. A torus can be viewed as a flexible rectangle rolled into … Continue reading

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A Torus and Its Dual, Part I

The torus is a familiar figure to many, so I chose a quick rotational period (5 seconds) for it. The dual of a torus — and I don’t know what else to call it — is not as familiar, so, … Continue reading

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A Zonish Polyhedron with 522 Faces, Together with Its 920-Faced Dual

The polyhedron above is a 522-faced zonish polyhedron, which resembles, but is not identical to, a zonohedron. True zonohedra are recognizable as that type of polyhedron by their exclusively zonogonal faces. Zonogons are polygons with even numbers of sites, and … Continue reading

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The Compounds of Five Octahedra and Five Cubes, and Related Polyhedra

This is the compound of five octahedra, each a different color. Since the cube is dual to the octahedron, the compound of five cubes, below, is dual to the compound above. Here are five cubes and five octahedra, compounded together, … Continue reading

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