Tag Archives: convex hull

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 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 icosidodecahedron. I use a program called Stella 4d … Continue reading

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Thirty-Four Rotating, Convex, and Non-Chiral Polyhedra with Icosidodecahedral Symmetry

Most in the field call this type of symmetry “icosahedral,” but I prefer the term George Hart uses — along with “cuboctahedral” in place of “octahedral.” Each polyhedral image here was created with Stella 4d: Polyhedron Navigator. At this linked … Continue reading

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A Polyhedral Journey, Beginning with the Snub Cube / Pentagonal Isositetrahedron Base/Dual Compound

The snub cube and its dual make an attractive compound. Since the snub cube is chiral, its chirality is preserved in this compound. If you examine the convex hull of this compound, you will find it to be chiral as … Continue reading

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A Collection of Unusual Polyhedra

In the post directly before this one, the third image was an icosahedral cluster of icosahedra. Curious about what its convex hull would look like, I made it, and thereby saw the first polyhedron I have encountered which has 68 … Continue reading

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A Polyhedral Investigation, Starting with an Augmentation of the Truncated Octahedron

If one starts with a central truncated octahedron, leaves its six square faces untouched, and augments its eight hexagonal faces with trianglular cupolae, this is the result. Seeing this, I did a quick check of its dual, and found it … Continue reading

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A Cluster of Nine Octahedra, and Related Polyhedra

If one starts with a central octahedron, then augments each of its eight triangular faces with identical octahedra, this is the result. It is then possible to augment each visible triangle of this cluster with yet more octahedra, which produces … Continue reading

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