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Tag Archives: dual
The Compound of the Truncated Isocahedron and the Pentakis Dodecahedron, with Related Polyhedra
The yellowandred polyhedron in the compound below is the truncated icosahedron, one of the Archimedean solids. The blue figure is its dual, the pentakis dodecahedron, which is one of the Catalan solids. The next image shows the convex hull of … Continue reading
Posted in Mathematics
Tagged compound, convex hull, dual, geometry, Mathematics, pentakis dodecahedron, polyhedra, polyhedron, truncated icosahedron
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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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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 mirrorimage 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 360Faced 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