quickfur wrote:Klitzing wrote:[...]

PS: it just occurs me, that quickfur might have thought of the diminished version of it, chopping off the layers (1) and (2) from the above, i.e. just to consider ..oxFx3..xfox5..xoxx&#xt only.

This then changes the corresponding total cell count into: 1 ti + 30 tets + 20 J92's + 12 peroes + 12 pecues + 60 squippies + 30 trips + 1 grid.

(Here they are again, the peroes or half-ids!)

Even better (more elementary) find!

--- rk

[...]

But anyway, if somebody can compute the coordinates for student91's new CRF, I can run it through my polyview viewer and render some nice images.

Alright, I got impatient today (and needed a break from calculating coordinates for the other constructions under consideration), so I figured out the coordinates for this CRF myself. Thanks to student91's lace tower, it's not that hard to compute these coordinates from the rectified 120-cell o5x3o3o. Since I already have the latter's coordinates, it's just a matter of sorting them by the first coordinate (since viewing from <5,0,0,0> is centered on an icosidodecahedron), and each different value corresponds with a layer in the lace tower. So it wasn't too difficult to identify the layer that needed to be replaced with x5x3x. Turns out that layer is identified by height 1+2*phi (for edge length 2, as is my custom). Replacement with x5x3x wasn't hard either, since I already have the coordinates on my website, so it was just a matter of prepending 1+2*phi to them.

Anyway, enough talk. Let's see some renders!

Here, we have the x5x3o (yellow), which is the cross-section of the o5x3o3o once the bistratic o5x3o cup has been removed from it. Immediately after this point, the 20 J92 cells begin, one of which is shown in magenta above. They fill up the .5.3x elements of the symmetry of the x5x3o. The x5.3. elements are filled up by 12 pentagonal rotundae (yes, there really are pentagonal rotundae ), one of which is shown in green here. These pentagonal rotundae are, in turn, linked to the pentagonal cupola that protrude outwards beyond the limb of the x5x3x, which is outlined in red here. These pentagonal cupola are interfaced to the J92's by triangular prism + 2 square pyramid combos, so again we see how triangular prisms and square pyramids play an important role in interfacing J92's to the pentagonal elements of the 120-cell family polytopes.

So according to my polytope viewer, there are 30 tetrahedra, 60 square pyramids, 30 triangular prisms, 12 pentagonal cupolae, 12 pentagonal rotundae, 1 x5x3x, 1 truncated dodecahedron, and 20 J92's, for a total of 166 cells. There are exactly 300 vertices (nice number!), 840 edges, and 706 polygons (440 triangles, 150 squares, 72 pentagons, 20 hexagons, 24 decagons).

P.S.: Here are the coordinates:

- Code: Select all
`# x5x3o`

<(7+3*sqrt(5))/2, 0, ±1, ±(5+3*sqrt(5))/2>

<(7+3*sqrt(5))/2, ±1, ±(5+3*sqrt(5))/2, 0>

<(7+3*sqrt(5))/2, ±(5+3*sqrt(5))/2, 0, ±1>

<(7+3*sqrt(5))/2, ±1, ±(3+sqrt(5))/2, ±(3+sqrt(5))>

<(7+3*sqrt(5))/2, ±(3+sqrt(5))/2, ±(3+sqrt(5)), ±1>

<(7+3*sqrt(5))/2, ±(3+sqrt(5)), ±1, ±(3+sqrt(5))/2>

<(7+3*sqrt(5))/2, ±(3+sqrt(5))/2, ±(1+sqrt(5)), ±(2+sqrt(5))>

<(7+3*sqrt(5))/2, ±(1+sqrt(5)), ±(2+sqrt(5)), ±(3+sqrt(5))/2>

<(7+3*sqrt(5))/2, ±(2+sqrt(5)), ±(3+sqrt(5))/2, ±(1+sqrt(5))>

# o5f3x:

<(5+3*sqrt(5))/2, 0, ±(7+3*sqrt(5))/2, ±1>

<(5+3*sqrt(5))/2, ±1, 0, ±(7+3*sqrt(5))/2>

<(5+3*sqrt(5))/2, ±(7+3*sqrt(5))/2, ±1, 0>

<(5+3*sqrt(5))/2, ±(1+sqrt(5))/2, ±(2+sqrt(5)), ±(3+sqrt(5))>

<(5+3*sqrt(5))/2, ±(2+sqrt(5)), ±(3+sqrt(5)), ±(1+sqrt(5))/2>

<(5+3*sqrt(5))/2, ±(3+sqrt(5)), ±(1+sqrt(5))/2, ±(2+sqrt(5))>

<(5+3*sqrt(5))/2, ±(3+sqrt(5))/2, ±(3+sqrt(5))/2, ±(5+3*sqrt(5))/2>

<(5+3*sqrt(5))/2, ±(3+sqrt(5))/2, ±(5+3*sqrt(5))/2, ±(3+sqrt(5))/2>

<(5+3*sqrt(5))/2, ±(5+3*sqrt(5))/2, ±(3+sqrt(5))/2, ±(3+sqrt(5))/2>

# x5o3F:

<3+sqrt(5), 0, ±(3+sqrt(5)), ±(3+sqrt(5))>

<3+sqrt(5), ±(3+sqrt(5)), 0, ±(3+sqrt(5))>

<3+sqrt(5), ±(3+sqrt(5)), ±(3+sqrt(5)), 0>

<3+sqrt(5), ±1, ±(7+3*sqrt(5))/2, ±(3+sqrt(5))/2>

<3+sqrt(5), ±(3+sqrt(5))/2, ±1, ±(7+3*sqrt(5))/2>

<3+sqrt(5), ±(7+3*sqrt(5))/2, ±(3+sqrt(5))/2, ±1>

<3+sqrt(5), ±(1+sqrt(5))/2, ±(5+3*sqrt(5))/2, ±(2+sqrt(5))>

<3+sqrt(5), ±(2+sqrt(5)), ±(1+sqrt(5))/2, ±(5+3*sqrt(5))/2>

<3+sqrt(5), ±(5+3*sqrt(5))/2, ±(2+sqrt(5)), ±(1+sqrt(5))/2>

# x5x3x (replaces previous o5f3f):

<1+2*phi> ~ apacs<1, 1, 4*phi+1>

<1+2*phi> ~ epacs<1, phi^3, 3+2*phi>

<1+2*phi> ~ epacs<2, phi^2, phi^4>

<1+2*phi> ~ epacs<phi^2, 3*phi, 2*phi^2>

<1+2*phi> ~ epacs<2*phi, 1+3*phi, 2+phi>

And here's the .off file for Marek.