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# Tag Archives: dual

## 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 polyhedron shown above. Any chiral polyhedron … Continue reading

Posted in Mathematics
Tagged chiral, compound, dual, geometry, Mathematics, polyhedra, polyhedron, stellate, stellation
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## 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.

## 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

## 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

## 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

## 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

Posted in Mathematics
Tagged dual, geometry, Mathematics, polyhedra, polyhedron, zonish, zonogon, zonohedra, zonohedron
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