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A Zonohedron with 3540 Faces, Together with Its Dual
Zonohedra are polyhedra made completely of faces which are zonogons. A zonogon is a polygon which: Has an even number of sides, Has opposite sides congruent, and Has opposite sides parallel....
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A Compound of Ten Elongated Octahedra Which Is Also a Particular Faceting of...
Thinking about the post immediately before this one led me to see if I could connect opposite triangular faces of a rhombicosidodecahedron to form a ten-part compound — and it worked with Stella 4d...
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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...
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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...
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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, for it, I...
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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...
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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...
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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...
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An Expansion of the Rhombic Enneacontahedron with 422 Faces, Together with...
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...
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The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part One
If you stellate the snub dodecahedron 43 times, this is the result. The yellow faces are kites, not rhombi. Like the snub dodecahedron itself, this polyhedron is chiral. Here is the mirror-image of the...
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