Search
Subject Categories:
 Art (423)
 Asperger's (32)
 Blogging (9)
 China and the Han (9)
 eBay (3)
 Education (89)
 Fiction (27)
 Geography (27)
 History (37)
 Humor (43)
 Life (352)
 Mandalas (119)
 Mathematics (1,174)
 Mental Health (71)
 Music (43)
 Mysteries (14)
 Politics (111)
 Quotations (63)
 Religion (58)
 Satire (7)
 Science and Scientists (115)
 Follow RobertLovesPi's Blog on WordPress.com
MostViewed Posts, Recently:

Recent Posts
 Meditating and Not
 Thoughts on Colonizing Space
 On Taxation, and Representation, in Public Education
 A Rhombic Dodecahedron, Made of Icosahedra, and Tall Triangular Antiprisms
 Honeycomb Made of Cuboctahedra and Octahedra
 Spectral Circles on a Cuboctahedron
 Spectral Circles on a Truncated Icosahedron
 Spectral Circles
 Heptagrammic
 June 13 Special Election in the PCSSD
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
 235,324 hits
Tag Archives: augmentation
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
On Polyhedral Augmentation and Excavation
I have made many posts here using polyhedral augmentation, but what I haven’t done — yet — is explain it. I have also neglected the reciprocal function of augmentation, which is called excavation. It is now time to fix both … Continue reading
Posted in Mathematics
Tagged augmentation, cluster, excavation, geometry, icosahedron, icosidodecahedron, Mathematics, polyhedra, polyhedral, polyhedron, reciprocal, solid
Leave a comment
The Compound of Five Cubes, Augmented with Thirty Snub Cubes: Three Versions
This clusterpolyhedron was made with Stella 4d, software you can try at this website. Above, it is colored by facetype, referring to each face’s position within the overall cluster. In the image below, the original compound of five cubes contained … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, cluster, compound, cube, five, geometry, Mathematics, polyhedra, polyhedral, polyhedron, snub cube
Leave a comment
A Truncated Icosahedron, with Hexagons Augmented By Triangular Pyramids, in a Chiral Pattern
I made this using Stella 4d: Polyhedron Navigator, software available here.
Posted in Mathematics
Tagged augmentation, augmented, chiral, chirality, geometry, Mathematics, polyhedra, polyhedron, truncated icosahedron
Leave a comment
A Great Icosahedron, Augmented with Twenty Icosahedra
The polyhedral clusters above and below use different coloringschemes, but are otherwise identical. Invisible, in the center, is a great icosahedron. Each of its faces has been augmented by a (Platonic) icosahedron. Both images were created using Stella 4d, software … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, geometry, great icosahedron, icosahedron, polyhedra, polyhedron
Leave a comment
The Greatly Augmented Rhombicosidodecahedron
I call this variant on the rhombicosidocahedron “greatly augmented” because it was formed by augmenting each pentagonal face of a central rhombicosidodecahedron with great dodecahedra, while each triangular face is augmented with great icosahedra. It was made using Stella 4d, … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, geometry, great, great dodecahedron, great icosahedron, greatly, Mathematics, polyhedra, polyhedron, rhombicosidodecahedron
1 Comment
A Polyhedral Investigation, Starting with an Augmentation of the Truncated Octahedron
If one starts with a central truncated octahedron, leaves its six square faces untouched, and augments its eight hexagonal faces with trianglular cupolae, this is the result. Seeing this, I did a quick check of its dual, and found it … Continue reading
Posted in Mathematics
Tagged augment, augmentation, convex hull, cupola, dual, truncated octahedron
2 Comments