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Tag Archives: stellation
Some Tetrahedral Stellations of the Truncated Cube
I created these with Stella 4d, which you may try for free at this website. To make a given polyhedral stellation appear larger, simply click on it.
Posted in Mathematics
Tagged cube, geometry, Mathematics, polyhedra, polyhedron, stellated, stellation, symmetry, tetrahedral, truncated
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Three Stellations of the Truncated Cube
The polyhedron above is the 12th stellation of the truncated cube. The one below is the 14th. The next one shown is the 18th and final stellation. If stellated again, the result is an ordinary truncated cube. These virtual models … Continue reading
Posted in Mathematics
Tagged geometry, Mathematics, polyhedra, polyhedron, stellated, stellating, stellation, truncated cube
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A Decorated Pentagonal Hexacontahedron, with Three of Its Stellations
This is a pentagonal hexacontahedron, the dual of the snub dodecahedron. It’s decorated with mandalas of the the type I blogged here, two posts ago. The mandalas do interesting things when this polyhedron is stellated, as you can see below. … Continue reading
Posted in Art, Mathematics
Tagged Art, geometric, geometrical, geometry, mathematical, Mathematics, pentagonal hexacontahedron, polyhedra, polyhedron, stellated, stellation
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Building a “Polyhedral Porcupine”
This is the icosahedron, followed by its first stellation. The first stellation of the icosahedron can be stellated again, and again, and so on. The “final stellation” of the icosahedron is the one right before the stellationseries “wraps around,” back … Continue reading
Posted in Mathematics
Tagged compound, final, geometry, icosahedron, Mathematics, polyhedra, polyhedral, polyhedron, porcupine, stellated, stellation
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Some Stellations of the Truncated Dodecahedron
The stellationseries of the truncated dodecahedron contains some interesting polyhedra. Selections from this series appear below. The polyhedron above is the 24th stellation of the truncated dodecahedron, while the one below is the 25th stellation. The polyhedron immediately above is the truncated … Continue reading
Posted in Mathematics
Tagged geometry, Mathematics, polyhedra, polyhedron, stellated, stellation, truncated dodecahedron
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The 11th, 13th, and 15th Stellations of the Icosahedron
First, this is the 11th stellation. Next, the 13th: And, finally, the 15th stellation of the icosahedron: I used Stella 4d, which you can find here, to make these.
Posted in Mathematics
Tagged geometry, icosahedron, Mathematics, polyhedra, polyhedral, polyhedron, stellated, stellation
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A Tetrahedral Exploration of the Icosahedron
Mathematicians have discovered more than one set of rules for polyhedral stellation. The software I use for rapidly manipulating polyhedra (Stella 4d, available here, including as a free trial download) lets the user choose between different sets of stellation criteria, … Continue reading
Posted in Mathematics
Tagged cuboctahedral, geometry, icosahedral, icosahedron, icosidodecahedral, Mathematics, octahedral, polyhedra, polyhedral, polyhedron, pyritohedral, solid, stellation, symmetry, tetrahedral
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