Search
Subject Categories:
 Art (462)
 Asperger's (32)
 Blogging (11)
 China and the Han (9)
 eBay (3)
 Education (93)
 Fiction (29)
 Geography (27)
 History (38)
 Humor (49)
 Life (363)
 Mandalas (126)
 Mathematics (1,275)
 Mental Health (74)
 Music (43)
 Mysteries (16)
 Politics (121)
 Quotations (64)
 Religion (58)
 Satire (12)
 Science and Scientists (121)
 Follow RobertLovesPi.net on WordPress.com
MostViewed Posts, Recently:

Recent Posts
 Octahedra and Cuboctahedra Can Fill Space Without Leaving Any Gaps
 Spectral Circles #3
 A Compound of the Great Stellated Dodecahedron and the Great Dodecahedron
 One Dozen Icosahedra
 Tessellation of Rhombi and Tetraconcave Octagons
 A Radial Tessellation Using Three Types of Rhombi
 A Radial Tessellation Using Two Types of Rhombi
 A Zonohedron with 1382 Faces, Based on the Rhombicosidodecahedron
 Spectral Circles #2
 Four Different Faceted Versions of the Rhombicosidodecahedron
Explore RobertLovesPi By Topic
 Arkansas
 Art
 Asperger's
 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
 life
 mandala
 mandalas
 math
 mathematical
 mathematical art
 Mathematics
 music
 nonagon
 octagon
 octahedron
 op art
 pentagon
 physics
 politics
 polygon
 polyhedra
 polyhedral
 polyhedron
 president
 quotation
 quote
 religion
 rhombi
 rhombic dodecahedron
 rhombicosidodecahedron
 rhombic triacontahedron
 rhombus
 school
 science
 snub dodecahedron
 star
 stellated
 stellation
 symmetry
 tessellation
 tetrahedron
 tiling
 triangle
 Trump
 truncated icosahedron
 USA
 words
 zonohedron
Hit Counter
 355,149 hits
Tag Archives: octahedra
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
Leave a comment
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
Leave a comment
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
Leave a comment
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
7 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