Search
Subject Categories:
 Art (449)
 Asperger's (32)
 Blogging (9)
 China and the Han (9)
 eBay (3)
 Education (91)
 Fiction (28)
 Geography (27)
 History (37)
 Humor (46)
 Life (358)
 Mandalas (122)
 Mathematics (1,223)
 Mental Health (72)
 Music (43)
 Mysteries (16)
 Politics (120)
 Quotations (64)
 Religion (58)
 Satire (10)
 Science and Scientists (120)
 Follow RobertLovesPi.net on WordPress.com
MostViewed Posts, Recently:

Recent Posts
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
 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
 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
 312,140 hits
Tag Archives: augmented
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 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
Icosidodecahedra, Icosahedra, and Dodecahedra
If one starts with a single icosidodecahedron, and then augments its pentagonal faces with dodecahedra, and its trianguar faces with icosahedra, this is the result. This figure has gaps in it where two pentagons and two triangles meet around a … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, cluster, dodecahedron, geometry, icosahedron, icosidodecahedron, Mathematics, polyhedra, polyhedral, polyhedron
Leave a comment
An Icosahedron, Augmented with Twenty Triangular Cupolae, Together with Its Dual
After making the above polyhedron using Stella 4d (a program you can try for free at http://www.software3d.com/Stella.php), I checked its dual, which is shown below. I was surprised at its appearance, for it resembles a stellated polyhedron, even though it … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, cupola, cupolae, dual, geometry, icosahedron, Mathematics, polyhedra, polyhedron, triangular
5 Comments