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...

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...

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...

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 ...

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...

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 ...

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...

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...

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....

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...

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...

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...

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...

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...

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 ...