Search found 71 matches

by Dinogeorge
Sun Feb 10, 2008 11:58 pm
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five great grand stellated hecatonicosachora

The ultimate regular aggrandizement of the hecatonicosachoron is constructed from the great grand hecatonicosachoron {5,5/2,3} by stellating its already huge great-dodecahedral cells into relatively enormous great stellated dodecahedra. The resulting figure, which has 600 vertices instead of the 120...
by Dinogeorge
Sun Feb 10, 2008 3:55 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five great grand hecatonicosachora

The terms “stellated,” “great,” and “grand” in the names of the regular star-polychora are commutative : It doesn’t matter in what order they are applied. In the context of the regular star-polytopes (which exist in two, three, and four dimensions), “stellated” refers to the edge-stellation of a reg...
by Dinogeorge
Fri Feb 08, 2008 11:56 pm
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five grand stellated hecatonicosachora

The next regular aggrandizement of the hecatonicosachoron arises by "stellation" (edge-stellation) of the grand hecatonicosachoron, so it is the “stellated grand hecatonicosachoron” or, in keeping with the tradition established by Arthur Cayley in naming the Kepler-Poinsot polyhedra, the grand stell...
by Dinogeorge
Thu Feb 07, 2008 9:04 pm
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

More on hecatonicosachoric aggrandizements

Unfortunately, Stella4D gets lost when I try to construct the vertex/cell-regular compounds of ten great stellated hecatonicosachora {5/2,3,5} and ten grand hecatonicosachora {5,3,5/2} from their vertex figures. Perhaps not coincidentally, these two polychora are each other's duals. These would have...
by Dinogeorge
Wed Feb 06, 2008 2:33 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Re: Five hexacosichora

For me, there are "edit" buttons next to the "quote" button in the top right corner of each post. As admin I see these on every post, but I thought other users would still be able to see these on their own posts, provided they are logged in. Is this not the case?. Ah, yes. I see them. Didn't notice...
by Dinogeorge
Tue Feb 05, 2008 4:22 pm
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Re: Five hexacosichora

robertw wrote:Just for your info, you can edit your old posts to correct errors.
Cool, but how? I don't see any "edit your post" buttons. :?
by Dinogeorge
Tue Feb 05, 2008 4:17 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Pictures

Incidentally, forum visitors may download for their own use any of my pictures by simply right-clicking on them and then left-clicking on the "save picture as" menu item. They're pretty snazzy when printed on glossy photoprint stock with an inkjet printer. :D
by Dinogeorge
Tue Feb 05, 2008 2:13 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Re: Five hexacosichora

here is the 0.555 section of the uniform polychoron dual of the E aggrandizement: http://members.aol.com/Dinogeorge/Ehecatonicosachoronduala.gif The uniform polychoron is color-coded to the vertex figure, but the E aggrandizement I left monochromatic. Oops! The color-coding was backward. I have put...
by Dinogeorge
Tue Feb 05, 2008 12:55 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five hexacosichora

In three-space, to obtain an icosahedron from a great dodecahedron’s surhedron, we simply fill up its 20 equit dimples with 20 flattened equit pyramids. These are not stellachunks of the great dodecahedron, because the “top” faces, opposite the low apex that sinks into the dimples, do not lie in the...
by Dinogeorge
Sat Feb 02, 2008 3:16 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five icosahedral hecatonicosachora

Over the years, a kind of unofficial terminology has evolved among people who play with polytopes. For example, in increasing order of dimensionality, there are four venerable names for the different kinds of polytope elements: vertex (plural: vertices), edge, face, and cell. This series has recentl...
by Dinogeorge
Fri Feb 01, 2008 7:11 pm
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Re: Five great hecatonicosachora

Dinogeorge wrote:And so on. Bruce Chilton has recently found all 57 stellalayers (A through BL) of the hecatonicosachoron.
Make that A through BE. Sorry about the typo!
by Dinogeorge
Sat Jan 26, 2008 6:23 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five great hecatonicosachora

The great hecatonicosachoron , Schlaefli symbol {5,5/2,5}, is only the second of the nonillions of aggrandizements of the regular hecatonicosachoron. Just as the stellated hecatonicosachoron may be modeled by sticking 120 dodecahedral pyramids onto the hecatonicosachoron’s dodecahedral cells, so the...
by Dinogeorge
Thu Jan 24, 2008 6:26 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five stellated hecatonicosachora

After typing this long post twice and completely destroying it twice , just because I accidentally happened to hit a wrong key at the website, I’ve learned my lesson and recomposed it using my word processor . That way I’ll at least have a copy to work on instead of losing the whole thing outright i...
by Dinogeorge
Wed Jan 23, 2008 7:52 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five hecatonicosachora

Here's a picture made from another of the cell-regular 4D compounds, the less complicated conjugate of the compound of five great grand stellated hecatonicosachora posted in a previous reply. Its five components are identical ordinary convex regular hecatonicosachora (120-cells), so the compound has...
by Dinogeorge
Tue Jan 22, 2008 7:30 am
Forum: Stella Forum
Topic: More 4D compounds now available
Replies: 51
Views: 98807

Five great grand hecatonicosachora

Here are a shot and a closeup of a 3D vertex-first (same as cell-first) section of the chiral compound of five great grand hecatonicosachora, {5,5/2,3}. The figure has the 600 corners of a hecatonicosachoron (120-cell), and a total of 600 great-dodecahedral cells. The vertex figure is a small stella...