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Tag Archives: icosahedron
Icosahedral Blue On Blue
Stella 4d was used to make this image, and you may try it for free by following this link.
Icosahedral Cluster
The great icosahedron, one of the KeplerPoinsot solids, is hidden from view at the center of this cluster. Each of its faces is augmented with a Platonic icosahedron, producing what you see here. Stella 4d is the software I used; … Continue reading
Posted in Mathematics
Tagged cluster, geometry, great, icosahedron, Mathematics, polyhedra, polyhedral, polyhedron
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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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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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Two Views of an Icosahedron, Augmented with Great Icosahedra
If colored by facetype, based on faceposition in the overall solid, this “cluster” polyhedron looks like this: There is another interesting view of this polyhedral cluster I like marginally better, though, and that is to separate the faces into colorgroups … Continue reading
Posted in Mathematics
Tagged cluster, geometry, great icosahedron, icosahedron, Mathematics, polyhedra, polyhedral, polyhedron
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On Polyhedral Augmentation and Excavation
I have made many posts here using polyhedral augmentation, but what I haven’t done — yet — is explain it. I have also neglected the reciprocal function of augmentation, which is called excavation. It is now time to fix both … Continue reading
Posted in Mathematics
Tagged augmentation, cluster, excavation, geometry, icosahedron, icosidodecahedron, Mathematics, polyhedra, polyhedral, polyhedron, reciprocal, solid
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