Oops, there is a problem - at least with the N=5 ursachoron based wedge
ofx3xoo5ooo&#xt || o3o5x!
That ursachoron itself, i.e.
ofx3xoo5ooo&#xt, is nothing but the 600-cell (=
ex) rotunda with the single vertex of the first and all the 20 vertices of the third vertex layer being diminished (i.e. a 21-diminishing of that rotunda).
Btw., that rotunda could be considered a tetra-stratic stack of 5 vertex layers:
o3o5o || x3o5o || o3o5x || f3o5o || o3x5o(where f would mark a tau scaled edge size).
Hence the dodecahedron, which is to be used as subdimensional opposite base of that wedge of consideration, would just be the 600-cell section at this very third layer. That is, the height (measured in the fifth direction orthogonal to the 4D base ursachoron) of that wedge is just zero! It thus becomes a degenerate flat 4D object only.
And true, all the lacing edges, being needed for the
x3o5o || o3o5x antiprism, are used as edges between the second and third vertex layer of the 600-cell (resp. its rotunda). And too, all the lacing edges, used in the
o3o5x || o3x5o (semi)cupola, are used in the 600-cell as edges connecting the third and the fifth vertex layer.
Given in a different way, here we'd have the lacing city not in the wedge-type way shown recently:
- Code: Select all
x3o5o
f3o5o o3o5x
o3x5o
but more metrically correct rather in a single (flat) stack:
- Code: Select all
x3o5o
o3o5x
f3o5o
o3x5o
(So far I have not looked into cases N=3 and N=4, so.)
--- rk