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Tag Archives: duality
Eight KiteRhombus Solids, Plus Five AllKite Polyhedra — the Convex Hulls of the Thirteen ArchimedeanCatalan Compounds
In a kiterhombus solid, or KRS, all faces are either kites or rhombi, and there are at least some of both of these quadrilateraltypes as faces. I have found eight such polyhedra, all of which are formed by creating the … Continue reading
Posted in Mathematics
Tagged Archimedean, Catalan, convex hull, dual, duality, geometry, kite, Mathematics, polyehdron, polyhedra, rhombi, rhombus, solid
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A TwiceZonohedrified Dodecahedron, Together with Its Dual
This polyhedron was created by performing vertexbased 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
Posted in Mathematics
Tagged dual, duality, geometry, Mathematics, polyhedra, polyhedron, zonohedra, zonohedron
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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 rhombusshaped panels which correspond … Continue reading
Posted in Mathematics
Tagged arithmetic, dual, duality, geometry, Mathematics, multiplication, multiply, nine, random, rhombic triacontahedron, thirty
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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 righthanded versions, known an entantiomers. They are mirrorimages of each other, like … Continue reading
Duality
Created with Stella 4d (site to try it: http://www.software3d.com/stella.php).
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.
Compound of the Dodecahedron and Its Dual, the Icosahedron
Software credit: see http://www.software3d.com/stella.php (free trial download available)