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Tag Archives: octahedron
Octahedra and Truncated Cubes Can Fill Space Without Leaving Any Gaps
I created this using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.
Posted in Mathematics
Tagged fill space, geometry, honeycomb, Mathematics, octahedra, octahedron, polyhedra, polyhedron, spacefilling, tessellation, truncated cube
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Octahedra and Cuboctahedra Can Fill Space Without Leaving Any Gaps
I created this image using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.
Posted in Mathematics
Tagged cuboctahedra, cuboctahedron, fill space, geometry, honeycomb, Mathematics, octahedra, octahedron, polyhedra, polyhedron, tesselation, tessellate
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The Compound of the Octahedron and the Small Stellated Dodecahedron
I made this rotating virtual model using Stella 4d: Polyhedron Navigator, which you can try for yourself at http://www.software3d.com/Stella.php. This solid is different from most twopart polyhedral compounds because an unusually high fraction of one polyhedron, the yellow octahedron, is … Continue reading
Posted in Mathematics
Tagged compound, geometry, Mathematics, octahedron, polyhedra, polyhedral, polyhedron, small stellated dodecahedron
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Some TenPart Polyhedral Compounds
While examining different facetings of the dodecahedron, I stumbled across one which is also a compound of ten elongated octahedra. Here’s what this compound looks like with the edges and vertices hidden: Next, I’ll put the edges and vertices back, … Continue reading
Posted in Mathematics
Tagged compound, cube, geometry, Mathematics, octahedra, octahedron, polyhedra, polyhedral, polyhedron
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A Compound of an Octahedron and a Pyritohedral Dodecahedron
I made this using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged compound, dodecahedron, geometry, Mathematics, octahedron, polyhedra, polyhedral, polyhedron, pyritohedral
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Honeycomb Made of Cuboctahedra and Octahedra
This is the threedimensional version of what is called a tessellation in two dimensions. It fills space, and can be continued in all directions. Software used: Stella 4d, available here.
Posted in Mathematics
Tagged cuboctahedra, cuboctahedron, geometry, honeycomb, lattice, Mathematics, octahedra, octahedron, polyhedra, polyhedron
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Augmenting the Octahedron with Octahedra, Repeatedly.
This is an octahedron. If you augment each face of an octahedron with more octahedra, you end up with this. One can then augment each triangular face of this with yet more octahedra. Here’s the next iteration: This could, of … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, geometry, Mathematics, octahedra, octahedron, polyehdral, polyhedra, polyhedron
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