Search found 71 matches
- Mon Feb 25, 2008 1:59 am
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
- Sun Feb 24, 2008 8:54 pm
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
- Sun Feb 24, 2008 6:52 pm
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
Up until now, the compounds have been rather more like ...
- Sun Feb 24, 2008 5:22 pm
- Forum: Polyhedra
- Topic: Compounds of cubes
- Replies: 8
- Views: 54599
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 = asin(1/√3) such that it ...
while the other one is a special version of 12B | S4 x I / C2 x I | μ , with μ = asin(1/√3) such that it ...
- Thu Feb 21, 2008 6:16 pm
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
- Thu Feb 21, 2008 7:03 am
- Forum: Polyhedra
- Topic: Compounds of cubes
- Replies: 8
- Views: 54599
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 ...
Then it took me a few more months to build a model. During ...
- Wed Feb 20, 2008 5:53 pm
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
- Wed Feb 20, 2008 8:08 am
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
- Tue Feb 19, 2008 11:30 pm
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
- Sun Feb 17, 2008 1:21 am
- Forum: Polyhedra
- Topic: Books about Polyhedra
- Replies: 10
- Views: 72902
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 ...
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 ...
- Sat Feb 16, 2008 11:14 pm
- Forum: Stella Forum
- Topic: Compounds of 10 regular polychora
- Replies: 12
- Views: 72024
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 ...
- Tue Feb 12, 2008 9:04 am
- Forum: Polyhedra
- Topic: What was your introduction to polyhedra?
- Replies: 21
- Views: 190476
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 ...
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 ...
- Tue Feb 12, 2008 8:25 am
- Forum: Polyhedron Models
- Topic: What's the most complex model you've ever made?
- Replies: 32
- Views: 299490
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 ...
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 ...
- Tue Feb 12, 2008 12:58 am
- Forum: Stella Forum
- Topic: More 4D compounds now available
- Replies: 51
- Views: 287931
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 ...
- Mon Feb 11, 2008 5:59 am
- Forum: Stella Forum
- Topic: More 4D compounds now available
- Replies: 51
- Views: 287931
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 ...