Tag Archives: duality

Eight Kite-Rhombus Solids, Plus Five All-Kite Polyhedra — the Convex Hulls of the Thirteen Archimedean-Catalan Compounds

In a kite-rhombus solid, or KRS, all faces are either kites or rhombi, and there are at least some of both of these quadrilateral-types as faces. I have found eight such polyhedra, all of which are formed by creating the … Continue reading

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A Twice-Zonohedrified Dodecahedron, Together with Its Dual

This polyhedron was created by performing vertex-based zonohedrifications of a dodecahedron — twice. The first zonohedrification produced a rhombic enneacontahedron, various version of which I have blogged many times before, but performing a second zonohedrification of the same type was … Continue reading

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A Polyhedral Demonstration of the Fact That Nine Times Thirty Equals 270, Along with Its Interesting Dual

It would really be a pain to count the faces of this polyhedron, in order to verify that there are 270 of them. Fortunately, it isn’t necessary to do so. The polyhedron above is made of rhombus-shaped panels which correspond … Continue reading

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The Pentagonal Hexacontahedron, and Related Polyhedra

As the dual of the snub dodecahedron, which is chiral, this member of the Catalan Solids is also chiral — in other words, it exists in left- and right-handed versions, known an entantiomers. They are mirror-images of each other, like … Continue reading

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Duality

Created with Stella 4d (site to try it: http://www.software3d.com/stella.php).

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Cuboctahedral Star

This is the dual of the previous post. Note: The software I used to create this is available as a free trial download at http://www.software3d.com/stella.php.

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Compound of the Dodecahedron and Its Dual, the Icosahedron

Software credit: see http://www.software3d.com/stella.php (free trial download available)

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