Acronym	n{4}2
Name	complex n-edged square
External links

The incidence matrix of the real encasing polytope (n,n-dip) is

xno xno   (n>2)

. . . .    | nn |   4 |  2  4 |  4
-----------+----+-----+-------+---
x . . .  & |  2 | 2nn |  1  2 |  3
-----------+----+-----+-------+---
xno . .  & |  n |   n | 2n  * |  2
x . x .    |  4 |   4 |  * nn |  2
-----------+----+-----+-------+---
xno x .  & ♦ 2n |  3n |  2  n | 2n

The incidence matrix of the complex polytope thus is

nn |  2
---+---
 n | 2n

Generators

with e  = exp(2πi/n),   E  = exp(2πi k/n),
where 1 < k < n and k not divisor of n

R0 = / e 0 \ ,  R1 = / 0 1 \
     \ 0 E /         \ 1 0 /

R0n  =  1                                  (rotation-rotation*)
R12  =  1                                  (exchange)
R0 * R1 * R0 * R1  =  R1 * R0 * R1 * R0    (rot. → up → rot.* → down  =  up → rot.* → down → rot.)