Search
Subject Categories:
 Art (421)
 Asperger's (32)
 Blogging (9)
 China and the Han (9)
 eBay (3)
 Education (88)
 Fiction (27)
 Geography (26)
 History (36)
 Humor (42)
 Life (350)
 Mandalas (118)
 Mathematics (1,169)
 Mental Health (70)
 Music (43)
 Mysteries (12)
 Politics (109)
 Quotations (63)
 Religion (58)
 Satire (7)
 Science and Scientists (114)
 Follow RobertLovesPi's Blog on WordPress.com
MostViewed Posts, Recently:

Recent Posts
 Heptagrammic
 June 13 Special Election in the PCSSD
 I used to donate occasionally to the ACLU, but then Donald Trump became president, so I set up a monthly payment plan.
 Augmenting the Octahedron with Octahedra, Repeatedly.
 Two Polyhedra, Each Featuring Enneagons and Octagons
 A Flock of 32 Rhombic Triacontahedra
 A Flock of Rhombicosidodecahedra
 It’s a Party in America . . . Tax Refunds Arrived!
 Op Art on a Dodecahedron
 Cyclops
Explore RobertLovesPi By Topic
Arkansas Art Asperger's Aspie astronomy atheism atheist chemistry chiral circle cluster compound cube cuboctahedron dodecahedron dual Education enneagon faceted faceting geometric geometrical geometrical art geometry Golden Ratio hexagon Humor humour icosahedron icosidodecahedral icosidodecahedron kite language life mandala mandalas math mathematical mathematical art Mathematics music nearmiss nonagon octagon octahedron op art pentagon physics politics polygon polyhedra polyhedral polyhedron quotation quote religion rhombic dodecahedron rhombicosidodecahedron rhombic triacontahedron rhombus school science snub dodecahedron star stellated stellation symmetry tessellation tetrahedron tiling triangle truncated icosahedron USA words zonohedronHit Counter
 230,463 hits
Tag Archives: octahedra
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
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
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
Leave a comment
Two Different FortyPart Polyhedral Compounds
The polyhedron above is a compound of twenty cubes and twenty octahedra, colored by symmetrybased facetype. If the same compound is viewed in “rainbow color mode,” it looks like this: With this particular compound, though, there are two versions — … Continue reading
Posted in Mathematics
Tagged 20, 40, compound, cube, forty, geometry, Mathematics, octahedra, octahedron, polyhedra, polyhedral, polyhedron, twenty
3 Comments
“Fractured” Octahedra
These are variations of the octahedron. I made them all with Stella 4d, which is available here. “Fractured” isn’t an official term, as “truncated or stellated” are, but I can’t come up with a better description, at least not yet. … Continue reading
Posted in Mathematics
Tagged fracture, fractured, geometry, Mathematics, octahedra, octahedron, polyhedra, polyhedron
Leave a comment
A Cluster of Nine Octahedra, and Related Polyhedra
If one starts with a central octahedron, then augments each of its eight triangular faces with identical octahedra, this is the result. It is then possible to augment each visible triangle of this cluster with yet more octahedra, which produces … Continue reading
Posted in Mathematics
Tagged augment, augmentation, cluster, convex hull, geometry, Mathematics, octahedra, octahedron, polyhedra, polyhedral, polyhedron, stellate, stellation
Leave a comment
An Octahedron, Augmented By Octahedra, and Then Reaugmented with Yet More Octahedra
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software I used to construct this cluster, three deep, of octahedra.