quickfur wrote:Keiji wrote:I'd say this was analogous to the square orthobicupola, which can be seen as the convex hull of a cuboid and octagon. The fact that the 8-cell is regular in the 4D version would be because of the √4 = 2 coincidence.quickfur wrote:Alright, I've finally discovered a real, valid, CRF augment of a duoprism. [...]

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Yeah it does resemble the square orthobicupola in some respects. Although in this case, you can't really decompose it into two cupolae. (Or can you??)

Sure you can!

Your finding is exactly what would be got by attaching those 2x K-4.73.1 (i.e. cube || {8}) at their octagons: You then omit all the 4 squacues (and the body of that octagon, which then won't connect to anything any longer). That is, you just keep the top (resp. the mirrored bottom) cube(s), the latterally attached trips, and the tets as partial complexes.

The now open boundaries will then be closed as follows. Note that the heights of K-4.73.1 were 1/2, thus the total height between the opposite cubes here equals 1! That is, you connect the 2 open faces of the original cubes by 2 further cubes, you connect the latterals of these ones to trips (used here as digonal cupolas) the lacings of which connect to the open faces of the trips of the former complex. And, at the lacing edges of the new cubes you attach tets, connecting 2 of their triangles to the new trips, and the other ones to the still open triangles of the tets of the former complex.

Note moreover, that the equatorial (body-less) octagon breaks the symmetry of the cubes in K-4.73.1. They just became 4-prisms. Likewise the 2 added cubes are similar 4-prisms (by their to be attached trips). Thus all 4 cubes (4-prisms) attach into a cycle of 4 (along that axial symmetry). And all fillings, i.e. either former K-4.73.1 and both added ones, are alike. This shows that you just could interchange "old" ones and "added" ones.

Now re-consider what this procedure was - placing it, per analogy, into a better seeable dimension.

Its kind of a figure like J91(= bilbiro = bilunabirotunda) : it re-uses partial shapes of known polyhedra. For J91 those were 2 parts of srid and 2 parts of id. But yours re-uses 4x the same part from just a single segmentochoron!

Nice indeed!

Finally, consider it as a lace city. Then your figure is just:

- Code: Select all
`x4o x4o`

x4x

x4o x4o

You might ask, why then is "{4} || J28" not contained in my paper about segmentochora? Well, it surely is a possible monostratic figure with unit edges only. Just that its base, J28, misses to be orbiform (vertices on a single sphere). And so would your finding thus too miss that attribution - as your provided coordinates did show likewise:

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apacs<1,1,1,1>

<±1, ±(1+sqrt(2)), 0, 0>

<±(1+sqrt(2)), ±1, 0, 0>

--- rk