n{4}2{3}2...2{3}2

Acronym	n{4}2{3}2...2{3}2
Name	complex n-edged hypercube (of complex d-dimensional space)
Confer	n{4}2 (d=2) n{4}2{3}2 (d=3) n{4}2{3}2{3}2 (d=4)

The incidence matrix of the complex polytope is derived as follows:

The vertex count is n^d
The subsequent following element counts each have one dimension less in n
and the prefactors will be the numbers in the Pascal triangle of the d-th row
(the last member of this row is omitted)
The subdiagonal rows are the element counts of the lower dimensional complex hypercubes,
in fact, the (d-k)-dimensional faces are appropriate dimensional complex hypercubes in turn
The superdiagonal rows are the element counts of the lower dimensional (real) simplices

Generators

R0ⁿ  =  1                                  (rotation-rotation*-rotation*-...)
Rn²  =  1                                  (exchange n & (n+1),   n > 0)
R0 * R1 * R0 * R1  =  R1 * R0 * R1 * R0    (rot. → up → rot.* → down  =  up → rot.* → down → rot.)
Rn * R(n+k)  =  R(n+k) * Rn                (k > 1,   n < d-k)
Rn * R(n+1) * Rn  =  R(n+1) * Rn * R(n+1)  (exchange n & (n+2),   n > 0)

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