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Tag Archives: convex hull
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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ThirtyFour Rotating, Convex, and NonChiral 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
Posted in Mathematics
Tagged convex hull, geometry, icosahedral symmetry, icosidodecahedral symmetry, Mathematics, polyhedra, polyhedron
2 Comments
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
Posted in Mathematics
Tagged chiral, chirality, compound, convex hull, dual, geometry, Mathematics, pentagonal icositetrahedron, polyhedra, polyhedron, snub cube, stellate, stellation
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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
Posted in Mathematics
Tagged convex hull, dual, geometry, Mathematics, polyhedra, polyhedron, stellate, stellation
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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
Posted in Mathematics
Tagged augment, augmentation, convex hull, cupola, dual, truncated octahedron
2 Comments