x-n-x     
x-n-o     x-n-o
     x-n-x     

The lace city display shows that this polychoron can be dissected vertically into segmentochoric components: into 2 n-pufs; thereby adding one 2n-prism as further facet each, which here occurs as internal pseudo facet only. In fact, the other way round, this polychoron well can be considered as an external blend of those 2 components.

Although the orientation as 2 parallel layers shows that those are all monostratic, but those would not be segmentochora. This is because of the needed shift of these non-degenerate bases out of their circumcenter. Accordingly there will be no (full-dimensional) circumradius either.

* One might include n=2 here as well. But there the pyramids become corealmic, getting different incidences. The resulting polychoron then would be nothing but the ope.

Note that the lines connecting the 2 wedges, i.e. y, as they are called bellow, are never meant to be contained here. Even for n=4, where y would happen to become unit sized. At n → 1.243647 resp. 5.104299 that y would become zero.

Incidence matrix according to Dynkin symbol

xx-n-ox&#x || xx-n-xo&#x (1.243647<n<5.104299)   → height = ???
n-cu || inv ortho n-cu

o.-n-o.      ..   ..    | n  *  * * | 2  2  2 0 0  0  0 0 0  0 0 | 1 2 1 2 1  2 0 0 0 0 0  0 0 0 0 0 | 1 2 1 1 0 0 0 0
.o-n-.o      ..   ..    | * 2n  * * | 0  1  0 1 1  1  1 0 0  0 0 | 0 1 1 0 0  1 1 1 1 1 1  1 0 0 0 0 | 1 1 1 0 1 1 1 0
..   ..      o.-n-o.    | *  * 2n * | 0  0  1 0 0  1  0 1 1  1 0 | 0 0 0 1 1  1 0 1 1 0 0  1 1 1 1 0 | 0 1 1 1 1 1 0 1
..   ..      .o-n-.o    | *  *  * n | 0  0  0 0 0  0  2 0 0  2 2 | 0 0 0 0 0  0 0 0 0 2 1  2 0 2 1 1 | 0 0 0 0 2 1 1 1
------------------------+-----------+----------------------------+-----------------------------------+----------------
x.   ..      ..   ..    | 2  0  0 0 | n  *  * * *  *  * * *  * * | 1 1 0 1 0  0 0 0 0 0 0  0 0 0 0 0 | 1 1 0 1 0 0 0 0
oo-n-oo&#x   ..   ..    | 1  1  0 0 | * 2n  * * *  *  * * *  * * | 0 1 1 0 0  1 0 0 0 0 0  0 0 0 0 0 | 1 1 1 0 0 0 0 0
o.-n-o.    || o.-n-o.    | 1  0  1 0 | *  * 2n * *  *  * * *  * * | 0 0 0 1 1  1 0 0 0 0 0  0 0 0 0 0 | 0 1 1 1 0 0 0 0
.x   ..      ..   ..    | 0  2  0 0 | *  *  * n *  *  * * *  * * | 0 1 0 0 0  0 1 1 0 1 0  0 0 0 0 0 | 1 1 0 0 1 0 1 0
..   .x      ..   ..    | 0  2  0 0 | *  *  * * n  *  * * *  * * | 0 0 1 0 0  0 1 0 1 0 1  0 0 0 0 0 | 1 0 1 0 0 1 1 0
.o-n-.o    || o.-n-o.    | 0  1  1 0 | *  *  * * * 2n  * * *  * * | 0 0 0 0 0  1 0 1 1 0 0  1 0 0 0 0 | 0 1 1 0 1 1 0 0
.o-n-.o    || .o-n-.o    | 0  1  0 1 | *  *  * * *  * 2n * *  * * | 0 0 0 0 0  0 0 0 0 1 1  1 0 0 0 0 | 0 0 0 0 1 1 1 0
..   ..      x.   ..    | 0  0  2 0 | *  *  * * *  *  * n *  * * | 0 0 0 1 0  0 0 1 0 0 0  0 1 1 0 0 | 0 1 0 1 1 0 0 1
..   ..      ..   x.    | 0  0  2 0 | *  *  * * *  *  * * n  * * | 0 0 0 0 1  0 0 0 1 0 0  0 1 0 1 0 | 0 0 1 1 0 1 0 1
..   ..      oo-n-oo&#x | 0  0  1 1 | *  *  * * *  *  * * * 2n * | 0 0 0 0 0  0 0 0 0 0 0  1 0 1 1 0 | 0 0 0 0 1 1 0 1
..   ..      .x   ..    | 0  0  0 2 | *  *  * * *  *  * * *  * n | 0 0 0 0 0  0 0 0 0 1 0  0 0 1 0 1 | 0 0 0 0 1 0 1 1
------------------------+-----------+----------------------------+-----------------------------------+----------------
x.-n-o.      ..   ..    | n  0  0 0 | n  0  0 0 0  0  0 0 0  0 0 | 1 * * * *  * * * * * *  * * * * * | 1 0 0 1 0 0 0 0
xx   ..&#x   ..   ..    | 2  2  0 0 | 1  2  0 1 0  0  0 0 0  0 0 | * n * * *  * * * * * *  * * * * * | 1 1 0 0 0 0 0 0
..   ox&#x   ..   ..    | 1  2  0 0 | 0  2  0 0 1  0  0 0 0  0 0 | * * n * *  * * * * * *  * * * * * | 1 0 1 0 0 0 0 0
x.   ..    || x.   ..    | 2  0  2 0 | 1  0  2 0 0  0  0 1 0  0 0 | * * * n *  * * * * * *  * * * * * | 0 1 0 1 0 0 0 0
..   o.    || ..   x.    | 1  0  2 0 | 0  0  2 0 0  0  0 0 1  0 0 | * * * * n  * * * * * *  * * * * * | 0 0 1 1 0 0 0 0
oo-n-oo&#x || o.-n-o.    | 1  1  1 0 | 0  1  1 0 0  1  0 0 0  0 0 | * * * * * 2n * * * * *  * * * * * | 0 1 1 0 0 0 0 0
.x-n-.x      ..   ..    | 0 2n  0 0 | 0  0  0 n n  0  0 0 0  0 0 | * * * * *  * 1 * * * *  * * * * * | 1 0 0 0 0 0 1 0
.x   ..    || x.   ..    | 0  2  2 0 | 0  0  0 1 0  2  0 1 0  0 0 | * * * * *  * * n * * *  * * * * * | 0 1 0 0 1 0 0 0
..   .x    || ..   x.    | 0  2  2 0 | 0  0  0 0 1  2  0 0 1  0 0 | * * * * *  * * * n * *  * * * * * | 0 0 1 0 0 1 0 0
.x   ..    || .x   ..    | 0  2  0 2 | 0  0  0 1 0  0  2 0 0  0 1 | * * * * *  * * * * n *  * * * * * | 0 0 0 0 1 0 1 0
..   .x    || ..   .o    | 0  2  0 1 | 0  0  0 0 1  0  2 0 0  0 0 | * * * * *  * * * * * n  * * * * * | 0 0 0 0 0 1 1 0
.o-n-.o    || oo-n-oo&#x | 0  1  1 1 | 0  0  0 0 0  1  1 0 0  1 0 | * * * * *  * * * * * * 2n * * * * | 0 0 0 0 1 1 0 0
..   ..      x.-n-x.    | 0  0 2n 0 | 0  0  0 0 0  0  0 n n  0 0 | * * * * *  * * * * * *  * 1 * * * | 0 0 0 1 0 0 0 1
..   ..      xx   ..&#x | 0  0  2 2 | 0  0  0 0 0  0  0 1 0  2 1 | * * * * *  * * * * * *  * * n * * | 0 0 0 0 1 0 0 1
..   ..      ..   xo&#x | 0  0  2 1 | 0  0  0 0 0  0  0 0 1  2 0 | * * * * *  * * * * * *  * * * n * | 0 0 0 0 0 1 0 1
..   ..      .x-n-.o    | 0  0  0 n | 0  0  0 0 0  0  0 0 0  0 n | * * * * *  * * * * * *  * * * * 1 | 0 0 0 0 0 0 1 1
------------------------+-----------+----------------------------+-----------------------------------+----------------
xx-n-ox&#x   ..   ..    ♦ n 2n  0 0 | n 2n  0 n n  0  0 0 0  0 0 | 1 n n 0 0  0 1 0 0 0 0  0 0 0 0 0 | 1 * * * * * * *
xx   ..&#x || x.   ..    ♦ 2  2  2 0 | 1  2  2 1 0  2  0 1 0  0 0 | 0 1 0 1 0  2 0 1 0 0 0  0 0 0 0 0 | * n * * * * * *
..   ox&#x || ..   x.    ♦ 1  2  2 0 | 0  2  2 0 1  2  0 0 1  0 0 | 0 0 1 0 1  2 0 0 1 0 0  0 0 0 0 0 | * * n * * * * *
x.-n-o.    || x.-n-x.    ♦ n  0 2n 0 | n  0 2n 0 0  0  0 n n  0 0 | 1 0 0 n n  0 0 0 0 0 0  0 1 0 0 0 | * * * 1 * * * *
.x   ..    || xx   ..&#x ♦ 0  2  2 2 | 0  0  0 1 0  2  2 1 0  2 1 | 0 0 0 0 0  0 0 1 0 1 0  2 0 1 0 0 | * * * * n * * *
..   .x    || ..   xo&#x ♦ 0  2  2 1 | 0  0  0 0 1  2  2 0 1  2 0 | 0 0 0 0 0  0 0 0 1 0 1  2 0 0 1 0 | * * * * * n * *
.x-n-.x    || .x-n-.o    ♦ 0 2n  0 n | 0  0  0 n n  0 2n 0 0  0 n | 0 0 0 0 0  0 1 0 0 n n  0 0 0 0 1 | * * * * * * 1 *
..   ..      xx-n-xo&#x ♦ 0  0 2n n | 0  0  0 0 0  0  0 n n 2n n | 0 0 0 0 0  0 0 0 0 0 0  0 1 n n 1 | * * * * * * * 1

yo ox xx-n-ox&#zx (1.243647<n<5.104299)   → height = 0
(tegum sum of (y,x)-n-p and ortho 2n-p)   y = sqrt[3 - 1/sin2(π/n)]

o. o. o.-n-o.    | 2n  * |  2  4  0  0  0 | 1  2  4  2 0 0 0 |  2  1 2
.o .o .o-n-.o    |  * 4n |  0  2  1  1  1 | 0  2  2  2 1 1 1 |  2  2 2
-----------------+-------+----------------+------------------+--------
.. .. x.   ..    |  2  0 | 2n  *  *  *  * | 1  0  2  0 0 0 0 |  1  0 2
oo oo oo-n-oo&#x |  1  1 |  * 8n  *  *  * | 0  1  1  1 0 0 0 |  1  1 1
.. .x ..   ..    |  0  2 |  *  * 2n  *  * | 0  2  0  0 1 1 0 |  2  2 0
.. .. .x   ..    |  0  2 |  *  *  * 2n  * | 0  0  2  0 1 0 1 |  2  0 2
.. .. ..   .x    |  0  2 |  *  *  *  * 2n | 0  0  0  2 0 1 1 |  0  2 2
-----------------+-------+----------------+------------------+--------
.. .. x.-n-o.    |  n  0 |  n  0  0  0  0 | 2  *  *  * * * * |  0  0 2
.. ox ..   ..&#x |  1  2 |  0  2  1  0  0 | * 4n  *  * * * * |  1  1 0
.. .. xx   ..&#x |  2  2 |  1  2  0  1  0 | *  * 4n  * * * * |  1  0 1
.. .. ..   ox&#x |  1  2 |  0  2  0  0  1 | *  *  * 4n * * * |  0  1 1
.. .x .x   ..    |  0  4 |  0  0  2  2  0 | *  *  *  * n * * |  2  0 0
.. .x ..   .x    |  0  4 |  0  0  2  0  2 | *  *  *  * * n * |  0  2 0
.. .. .x-n-.x    |  0 2n |  0  0  0  n  n | *  *  *  * * * 2 |  0  0 2
-----------------+-------+----------------+------------------+--------
.. ox xx   ..&#x ♦  2  4 |  1  4  2  2  0 | 0  2  2  0 1 0 0 | 2n  * *
.. ox ..   ox&#x ♦  1  4 |  0  4  2  0  2 | 0  2  0  2 0 1 0 |  * 2n *
.. .. xx-n-ox&#x ♦  n 2n |  n 2n  0  n  n | 1  0  n  n 0 0 1 |  *  * 4