Search found 71 matches

by Dinogeorge
Mon Feb 25, 2008 1:59 am
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Ten great grand hecatonicosachora

This, as far as I know, is “humanity’s first look” at the compound of ten great grand hecatonicosachora in a hecatonicosachoron . As with the preceding compound, I painted it with just two colors (turquoise and red), one for each chiral subset of five. Where the external facelets are coplanar, the c...
by Dinogeorge
Sun Feb 24, 2008 8:54 pm
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Ten great grand stellated hecatonicosachora

This, as far as I know, is “humanity’s first look” at the spectacular compound of ten great grand stellated hecatonicosachora about a hexacosichoron . As with the preceding compound, I painted it with just two colors (white and red), one for each chiral subset of five. Where the external facelets ar...
by Dinogeorge
Sun Feb 24, 2008 6:52 pm
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Missing ten-compounds

Here is where I would have continued with the compounds of ten great stellated hecatonicosachora and grand hecatonicosachora in a hecatonicosachoron , but so far my efforts to coax Stella4D into displaying them for me have come to naught. Up until now, the compounds have been rather more like "lumpy...
by Dinogeorge
Sun Feb 24, 2008 5:22 pm
Forum: Polyhedra
Topic: Compounds of cubes
Replies: 8
Views: 27410

Compounds of 12 cubes

The first model you show is a special position of 12A | S4 x I / C2 x I | μ , for which μ = acos(1/√3) such that it can be divided into 3 x 4 | D12 x I / D3 x I or into 4 x 3 | D12 x I / D4 x I while the other one is a special version of 12B | S4 x I / C2 x I | μ , with μ ...
by Dinogeorge
Thu Feb 21, 2008 6:16 pm
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Ten hexacosichora

This, as far as I know, is “humanity’s first look” at the compound of ten hexacosichora in a hecatonicosachoron . As with the preceding compound, I painted it with just two colors (dark blue and red), one for each chiral subset of five. Where the external facelets are coplanar, the colors blend into...
by Dinogeorge
Thu Feb 21, 2008 7:03 am
Forum: Polyhedra
Topic: Compounds of cubes
Replies: 8
Views: 27410

Challenging model

As a student I found my first compound of twelve cubes and it took me more than half a year to calculate (using standard algebra) the shape of the individual pieces. After that I still didn't have any clue of how the polyhedron would look. Then it took me a few more months to build a model. During ...
by Dinogeorge
Wed Feb 20, 2008 5:53 pm
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Ten icosahedral hecatonicosachora

This, as far as I know, is “humanity’s first look” at the compound of ten icosahedral hecatonicosachora in a hecatonicosachoron . As with the preceding compound, I painted it with just two colors (light blue and maroon), one for each chiral subset of five. Where the external facelets are coplanar, t...
by Dinogeorge
Wed Feb 20, 2008 8:08 am
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Ten great hecatonicosachora

This, as far as I know, is “humanity’s first look” at the compound of ten great hecatonicosachora in a hecatonicosachoron . As with the preceding compound, I painted it with just two colors (light yellow and red), one for each chiral subset of five. Where the external facelets are coplanar, the colo...
by Dinogeorge
Tue Feb 19, 2008 11:30 pm
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Ten stellated hecatonicosachora

And here is “humanity’s first look” at the compound of ten stellated hecatonicosachora in a hecatonicosachoron . As with the preceding compound, I painted it with just two colors (lavender pink and teal), one for each chiral subset of five. Where the external facelets are coplanar, the colors blend....
by Dinogeorge
Sun Feb 17, 2008 1:21 am
Forum: Polyhedra
Topic: Books about Polyhedra
Replies: 10
Views: 38182

More books

Marcel's list contains some truly inspirational books. Let me add: The first book I read featuring polyhedron models was Cundy & Rollett's Mathematical Models , the first edition of which Bruce Chilton loaned me for a few weeks back in 1958 when I was in eighth grade. I picked up a copy of the seco...
by Dinogeorge
Sat Feb 16, 2008 11:14 pm
Forum: Stella Forum
Topic: Compounds of 10 regular polychora
Replies: 12
Views: 40237

Ten hecatonicosachora

Well, here’s “humanity’s first look” at the cell-regular compound of ten hecatonicosachora about a hexacosichoron , displayed as the 0.555 section by a realm orthogonal to an icosahedral symmetry axis. I painted it in two colors, one for each chiral subset of five hecatonicsachora. All the compounds...
by Dinogeorge
Tue Feb 12, 2008 9:04 am
Forum: Polyhedra
Topic: What was your introduction to polyhedra?
Replies: 21
Views: 60837

Re: Six pentagrammatic prisms

Do you notice a certain similarity to Miller's Monster? Sure. The compound of twelve pentagrammatic prisms is a faceting of the rhombicosidodecahedron, and Miller's monster is a faceting of a quasiuniform rhombicosidodecahedron in which the rhombi-squares are made into just a little off-square rect...
by Dinogeorge
Tue Feb 12, 2008 8:25 am
Forum: Polyhedron Models
Topic: What's the most complex model you've ever made?
Replies: 29
Views: 104481

Re: What's the most complex model you've ever made?

What's the most complex model you've ever made :?: With my own hands it was a Miller's monster about a foot across, which I enameled in seven colors. I couldn't carry it across the continent when I moved from Toronto to San Diego, so I left it (and a few other models) with Coxeter. It was the first...
by Dinogeorge
Tue Feb 12, 2008 12:58 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five grand hexacosichora

The great icosahedron is the most complicated of the regular polyhedra in terms of the number of its external facelets, with a surhedron of 180 faces. Its 4D analogue, the grand hexacosichoron (600-cell) likewise is the most complicated of the regular polychora, with a surchoron of 36000 cells (acco...
by Dinogeorge
Mon Feb 11, 2008 5:59 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five great icosahedral hecatonicosachora

There are two cute ways to construct the regular star-polychoron {3,5/2,5}. One is to greaten each of the 120 icosahedral cells of {3,5,5/2}, the icosahedral hecatonicosachoron, into relatively huge great icosahedra. Then the 20 equit faces of each icosahedral cell naturally expand (“greaten”) into ...