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Tag Archives: octahedron
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
1 Comment
A Crinkled Octahedron
“Crinkled” is merely descriptive; I offer no mathematical definition of the term. This was a polyhedron I stumbled along while doing randomwalk polyhedral manipulations with Stella 4d, available at this website.
Posted in Art, Mathematics
Tagged crinkle, crinkled, geometry, Mathematics, octahedron, polyhedra, polyhedron
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Hexastar Octahedron
I wish I remembered exactly how I made this polyhedron, but I don’t. I found it during a “random walk” polyhedral exploration using Stella 4d: Polyhedron Navigator, software you can buy, or try for free, here.
Open Octahedral Lattice of Cubes and Rhombicosidodecahedra
This pattern could be continued, indefinitely, into space. Here is a second view, in rainbow color mode, and with all the squares hidden. [These images were created with Stella 4d, software you may buy — or try for free — … Continue reading
Posted in Art, Mathematics
Tagged Art, cube, geometric, geometrical, geometry, lattice, mathematical, Mathematics, octahedral, octahedron, polyhedra, polyhedral, polyhedron, rhombicosidodecahedron
1 Comment
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 octahedra, compounded together, … Continue reading
Posted in Mathematics
Tagged compound, cubes, dual, geometry, Mathematics, octahedra, octahedron, polyhedra, polyhedron, stellated, stellation
2 Comments
Building a Rhombic Enneacontahedron, Using Icosahedra and Elongated Octahedra
With four icosahedra, and four octahedra, it is possible to attach them to form this figure: This figure is actually a rhombus, but the gap between the two central icosahedra is so small that this is hard to see. To … Continue reading
Posted in Mathematics
Tagged build, building, construct, constructing, construction, elongated, geometry, icosahedron, Mathematics, octahedron, polyhedra, polyhedron, rhombic enneacontahedron
4 Comments