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Tag Archives: facet
A Faceting of the Rhombcuboctahedron
This particular faceting of the rhombcuboctahedron can also be viewed as a cluster of stella octangulae. I made it using Stella 4d, polyhedronmanipulating software you can try, for yourself, at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged facet, faceted, faceting, geometry, Mathematics, polyhedra, polyhedron, rhombcuboctahedron, rhombicuboctahedron, stella octangula
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Standard and Faceted Versions, Side by Side, of Each of the Thirteen Archimedean Solids
These two polyhedra are the truncated tetrahedron on the left, plus at least one faceted version of that same Archimedean solid on the right. As you can see, in each case, the figures have the same set of vertices — … Continue reading
Posted in Mathematics
Tagged Archimedean, chiral, chirality, compound, facet, faceted, faceting, geometry, Mathematics, polyhedra, polyhedral, polyhedron, solid
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A Compound of Ten Elongated Octahedra Which Is Also a Particular Faceting of the Rhombicosidodecahedron, Together with Its Dual
Thinking about the post immediately before this one led me to see if I could connect opposite triangular faces of a rhombicosidodecahedron to form a tenpart compound — and it worked with Stella 4d just as it had when I … Continue reading
Posted in Mathematics
Tagged 10, compound, dual, elongated, facet, faceted, faceting, geometry, Mathematics, octahedra, polyhedra, polyhedron, rhombicosidodecahedron, ten
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One of Many Possible Facetings of the Rhombic Triacontahedron
The simplest way I can explain faceting is that it takes a familiar polyhedron’s vertices, and then connects them in unusual ways, so that you obtain different edges and faces. If you take the convex hull of a faceted polyhedron, … Continue reading
Posted in Mathematics
Tagged facet, faceted, faceting, geometry, Mathematics, polyhedra, polyhedron, rhombic triacontahedron
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Four Different Facetings of the Great Rhombcuboctahedron
All four of these rotating images were created using software called Stella 4d: Polyhedron Navigator. You can buy this program, or try it for free, at this website. Faceting is the inverse function of stellation, and involves connecting the vertices … Continue reading
Posted in Mathematics
Tagged facet, faceted, faceting, geometry, great, icosidodecahedron, Mathematics, polyhedra, polyhedron, rhombcuboctahedron, rhombicuboctahedron, truncated
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There Are Many Faceted Versions of the Dodecahedron. This One Is the Dual of the Third Stellation of the Icosahedron.
The twelve purple faces of this faceted dodecahedron show up on Stella 4d‘s control interface as {10/4} star decagons, which would make them each have five pairs of two coincident vertices. I’m informally naming this special decagonthatlookslikeapentagram (or “star pentagon,” … Continue reading
Posted in Mathematics
Tagged antipentagram, decagon, dodecahedron, dual, facet, faceted, faceting, geometry, icosahedron, Mathematics, pentagram, polyhedra, polyhedron, star decagon, stellation, Third, {10/4}
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One Faceting, Each, of the Snub Cube and Snub Dodecahedron
These are facetings of the snub cube (above) and snub dodecahedron (below). I made both using Stella 4d, software you can try for yourself right here.
Posted in Mathematics
Tagged facet, faceted, faceting, geometry, Mathematics, polyehdra, polyhedron, snub cube, snub dodecahedron
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