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Tag Archives: faceting
A Hollow Faceting of the Rhombicosidodecahedron, and Its Hollow Dual
The images above all show a particular faceting of the rhombicosidodecahedron which, to my surprise, is hollow. It has the vertices of a rhombicosidodecahedron, but two different facetypes, as seen in the smaller pictures: yellow hexagons, and red isosceles trapezoids. … Continue reading
Posted in Mathematics
Tagged faceted, faceting, geometry, hollow, Mathematics, polyhedra, polyhedron, puzzle
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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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Five Faceted Polyhedra
Above, on the left, is a faceted cuboctahedron. To its right are a faceted snub dodecahedron (upper right) which is also a tenpart compound, and a faceted truncated cube below that. Any of these images may be enlarged by clicking … Continue reading
Posted in Mathematics
Tagged faceted, faceting, geometry, Mathematics, polyhedra, polyhedron
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Multiple Facetings of the Icosidodecahedron
To create a faceted icosidodecahedron, you simply start with an icosidodecahedron, then remove its edges and faces. Next, you connect the vertices differently, thus creating new faces and edges. As you can see below, this can be done in many … Continue reading
Posted in Mathematics
Tagged faceted, faceting, geometry, icosidodecahedron, Mathematics, polyhedra, polyhedron
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A Faceted Icosidodecahedron with 48 Faces
The 48 faces of this faceted icosidodecahedron are: 6 green regular decagons (difficult to see, because they pass through the figure’s center) 30 golden rectangles, shown in yellow, and each interpenetrating other faces 12 blue star pentagons Software called Stella 4d … Continue reading
Posted in Mathematics
Tagged faceted, faceting, geometry, Golden Rectangle, icosidodecahedron, Mathematics, polyhedra, polyhedron, star pentagon
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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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A Compound of Fifteen Cuboids — Which Is Also a Particular Faceting of the Icosidodecahedron
The creator of Stella 4d, the program I used to make these rotating polyhedral images, is Robert Webb (and the software itself may be tried for free here). Recently, on Facebook, he displayed a paper model of this compound of … Continue reading
Posted in Mathematics
Tagged 15, compound, cuboids, faceted, faceting, fifteen, geometry, icosidodecahedron, Mathematics, polyhedra, polyhedron
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