Acronym n-pidpy Name n-prismatic bipyramid Lace cityin approx. ASCII-art x-n-o o-n-o o-n-o x-n-o Especially tript (n=3)   cute (n=4)   pipt (n=5) Confer related segmentochora: n-pipy

The lace city display shows that this polychoron can be dissected vertically into segmentochoric components: into 2 pt||n-p; thereby adding one n-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.

As degenerate subdimensional case one might include n=2 here somehow as well. Then the pyramids become corealmic, the resulting polyhedron would be nothing but the oct.

Note that the line connecting the 2 tips, i.e. y, as it is called bellow, is never meant to be contained here. Even for n=4, where y would happen to become unit sized. At n → 5.104299 that y would become zero.

Incidence matrix according to Dynkin symbol

ox-n-oo&#x || xo-n-oo&#x (2<n<5.104299)   → height = ???
n-py || inv ortho n-py

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

yo ox ox-n-oo&#zx (2<n<5.104299)   → height = 0
(tegum sum of y-line and perp n-p)   y = sqrt[3 - 1/sin2(π/n)]
(tegum product of y-line with n-p)

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