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The Truncated Stella Octangula
This can also be called the compound of two truncated tetrahedra. This image was created using Stella 4d, which you can try at this website.Filed under: Mathematics Tagged: 2, compound, geometry,...
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The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part One
If you stellate the snub dodecahedron 43 times, this is the result. The yellow faces are kites, not rhombi. Like the snub dodecahedron itself, this polyhedron is chiral. Here is the mirror-image of the...
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A Compound of Two Stellated Polyhedra
I made this using Stella 4d, software you can try for free at http://www.software3d.com/Stella.php. Filed under: Mathematics Tagged: compound, geometry, Mathematics, polyhedra, polyhedron, stellated
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Twisted Polyhedral Compound
I used Stella 4d to make this. You may try this program for free at http://wwwsoftware3d.com/Stella.php.Filed under: Mathematics Tagged: compound, geometry, Mathematics, polyhedra, polyhedral,...
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A Chiral Polyhedron with Tetrahedral Symmetry
The yellow faces of this polyhedron are parallelograms, while the red ones are trapezoids. To demonstrate its chirality, here is the compound of it, and its own mirror-image. Both of these “virtual...
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The Compound of the Rhombic Dodecahedron and Its Own Third Stellation
I used Stella 4d to make this polyhedral compound, and this program may be tried for free at this website.Filed under: Mathematics Tagged: compound, geometry, Mathematics, polyhedra, 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...
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Compound of Two Tetrahedral Wedges
I made this with Stella 4d, a program you can try for yourself right here.Filed under: Mathematics Tagged: compound, geometry, Mathematics, polyhedra, polyhedral, polyhedron, tetrahedra, tetrahedron,...
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The Compound of the Dodecahedron and the First Stellation of the Icosahedron
I made this using Stella 4d, available here.Filed under: Mathematics Tagged: compound, geometry, Mathematics, polyhedra, polyhedron
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Compound of Three Tetrahedral Wedges
Software used: Stella 4d, available here.Filed under: Mathematics Tagged: compound, geometry, Mathematics, polyhedra, polyhedron, tetrahedra, tetrahedron
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The Snub Dodecahedron and Related Polyhedra, Including Compounds
The dual of the snub dodecahedron (above) is called the pentagonal hexacontahedron (below, left). The compound of the two is shown below, at right. (Any of the smaller images here may be enlarged with...
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Standard and Faceted Versions, Side by Side, of Each of the Thirteen...
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...
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A Torus and Its Dual, Part I
The torus is a familiar figure to many, so I chose a quick rotational period (5 seconds) for it. The dual of a torus — and I don’t know what else to call it — is not as familiar, so, for it, I...
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Two Compounds of Skewed Polyhedra, Each with Twelve Total Faces in the Compound
I found both of these with what one could call “random-walk playing” with polyhedral-manipulation software, Stella 4d, available here, with a free trial-download available. In the figure above, both...
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A Compound of Two Pyritohedral Dodecahedra
I made this compound using Stella 4d, a program which is available here: http://www.software3d.com/Stella.php.Filed under: Mathematics Tagged: compound, dodecahedra, dodecahedron, geometry,...
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The Compounds of Five Octahedra and Five Cubes, and Related Polyhedra
This is the compound of five octahedra, each a different color. Since the cube is dual to the octahedron, the compound of five cubes, below, is dual to the compound above. Here are five cubes and five...
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A Hollow, Five-Color Version of the Compound of Five Rhombic Dodecahedra
I made this using Stella 4d, software you can find at http://www.software3d.com/Stella.php.Filed under: Mathematics Tagged: compound, five, geometry, Mathematics, polyhedra, polyhedron, rhombic...
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A Compound of Ten Thin Parallelopipeds, Together with Its Final Stellation
The polyhedron above also appeared in the post immediately before this one, as the second of three images. However, here it is presented in “rainbow color mode.” This is its final stellation: Both...
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A Compound of Ten Elongated Octahedra Which Is Also a Particular Faceting of...
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 ten-part compound — and it worked with Stella 4d...
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A Compound of Fifteen Cuboids — Which Is Also a Particular Faceting of the...
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...
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