Acronym n-cuf Name n-gonal cupofastegium,2n-gon - n-prismatic wedge,n-gonal orthobicupolaic ring,{2n} || n-prism,{n} || n-cupola Segmentochoron display Circumradius sqrt[(5+2 cos(π/n)-4cos2(π/n))/(8-12 cos2(π/n))] Lace cityin approx. ASCII-art ``` x-n-x x-n-o x-n-o ``` Especially {4} || ortho {4} (n=2)*   {6} || trip (n=3)   {8} || cube (n=4)   {10} || pip (n=5) Confer more general: {n/d}-cuf   general polytopal classes: segmentochora

* The case n=2 equally would be considerable here by concept, it just has a different incidence matrix as the n-gons become degenerate.

Incidence matrix according to Dynkin symbol

```xx-n-ox xo&#x   (2 < n < 5.104299)   → height = sqrt[3 - 1/sin2(π/n)]/2
(n-p || {2n})

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

```xxx-n-oxo&#x   → height(1,2) = height(2,3) = sqrt[4 - 1/sin2(π/n)]/2
height(1,3) = 1

o..-n-o..    | n  * * | 2  2 1 0 0  0 0 | 1 2 1 2  2 0 0 0 0 | 1 1 2 1 0
.o.-n-.o.    | * 2n * | 0  1 0 1 1  1 0 | 0 1 1 0  1 1 1 1 0 | 1 0 1 1 1
..o-n-..o    | *  * n | 0  0 1 0 0  2 2 | 0 0 0 2  2 0 2 1 1 | 0 1 2 1 1
-------------+--------+-----------------+--------------------+----------
x..   ...    | 2  0 0 | n  * * * *  * * | 1 1 0 1  0 0 0 0 0 | 1 1 1 0 0
oo.-n-oo.&#x | 1  1 0 | * 2n * * *  * * | 0 1 1 0  1 0 0 0 0 | 1 0 1 1 0
o.o-n-o.o&#x | 1  0 1 | *  * n * *  * * | 0 0 0 2  2 0 0 0 0 | 0 1 2 1 0
.x.   ...    | 0  2 0 | *  * * n *  * * | 0 1 0 0  0 1 1 0 0 | 1 0 1 0 1
...   .x.    | 0  2 0 | *  * * * n  * * | 0 0 1 0  0 1 0 1 0 | 1 0 0 1 1
.oo-n-.oo    | 0  1 1 | *  * * * * 2n * | 0 0 0 0  1 0 1 1 0 | 0 0 1 1 1
..x   ...    | 0  0 2 | *  * * * *  * n | 0 0 0 1  0 0 1 0 1 | 0 1 1 0 1
-------------+--------+-----------------+--------------------+----------
x..-n-o..    | n  0 0 | n  0 0 0 0  0 0 | 1 * * *  * * * * * | 1 1 0 0 0
xx.   ...&#x | 2  2 0 | 1  2 0 1 0  0 0 | * n * *  * * * * * | 1 0 1 0 0
...   ox.&#x | 1  2 0 | 0  2 0 0 1  0 0 | * * n *  * * * * * | 1 0 0 1 0
x.x   ...&#x | 2  0 2 | 1  0 2 0 0  0 1 | * * * n  * * * * * | 0 1 1 0 0
ooo-n-ooo&#x | 1  1 1 | 0  1 1 0 0  1 0 | * * * * 2n * * * * | 0 0 1 1 0
.x.-n-.x.    | 0 2n 0 | 0  0 0 n n  0 0 | * * * *  * 1 * * * | 1 0 0 0 1
.xx   ...&#x | 0  2 2 | 0  0 0 1 0  2 1 | * * * *  * * n * * | 0 0 1 0 1
...   .xo&#x | 0  2 1 | 0  0 0 0 1  2 0 | * * * *  * * * n * | 0 0 0 1 1
..x-n-..o    | 0  0 n | 0  0 0 0 0  0 n | * * * *  * * * * 1 | 0 1 0 0 1
-------------+--------+-----------------+--------------------+----------
xx.-n-ox.&#x ♦ n 2n 0 | n 2n 0 n n  0 0 | 1 n n 0  0 1 0 0 0 | 1 * * * *
x.x-n-o.o&#x ♦ n  0 n | n  0 n 0 0  0 n | 1 0 0 n  0 0 0 0 1 | * 1 * * *
xxx   ...&#x ♦ 2  2 2 | 1  2 2 1 0  2 1 | 0 1 0 1  2 0 1 0 0 | * * n * *
...   oxo&#x ♦ 1  2 1 | 0  2 1 0 1  2 0 | 0 0 1 0  2 0 0 1 0 | * * * n *
.xx-n-.oo&#x ♦ 0 2n n | 0  0 0 n n 2n n | 0 0 0 0  0 1 n n 1 | * * * * 1
```
```or
o..-n-o..     & | 2n  * |  2  2 1 0 0 | 1  2  1 2  2 0 | 1 1 2 1
.o.-n-.o.       |  * 2n |  0  2 0 1 1 | 0  2  2 0  1 1 | 2 0 1 1
----------------+-------+-------------+----------------+--------
x..   ...     & |  2  0 | 2n  * * * * | 1  1  0 1  0 0 | 1 1 1 0
oo.-n-oo.&#x  & |  1  1 |  * 4n * * * | 0  1  1 0  1 0 | 1 0 1 1
o.o-n-o.o&#x    |  2  0 |  *  * n * * | 0  0  0 2  2 0 | 0 1 2 1
.x.   ...       |  0  2 |  *  * * n * | 0  2  0 0  0 1 | 2 0 1 0
...   .x.       |  0  2 |  *  * * * n | 0  0  2 0  0 1 | 2 0 0 1
----------------+-------+-------------+----------------+--------
x..-n-o..     & |  n  0 |  n  0 0 0 0 | 2  *  * *  * * | 1 1 0 0
xx.   ...&#x  & |  2  2 |  1  2 0 1 0 | * 2n  * *  * * | 1 0 1 0
...   ox.&#x  & |  1  2 |  0  2 0 0 1 | *  * 2n *  * * | 1 0 0 1
x.x   ...&#x    |  4  0 |  2  0 2 0 0 | *  *  * n  * * | 0 1 1 0
ooo-n-ooo&#x    |  2  1 |  0  2 1 0 0 | *  *  * * 2n * | 0 0 1 1
.x.-n-.x.       |  0 2n |  0  0 0 n n | *  *  * *  * 1 | 2 0 0 0
----------------+-------+-------------+----------------+--------
xx.-n-ox.&#x  & ♦  n 2n |  n 2n 0 n n | 1  n  n 0  0 1 | 2 * * *
x.x-n-o.o&#x    ♦ 2n  0 | 2n  0 n 0 0 | 2  0  0 n  0 0 | * 1 * *
xxx   ...&#x    ♦  4  2 |  2  4 2 1 0 | 0  2  0 1  2 0 | * * n *
...   oxo&#x    ♦  2  2 |  0  4 1 0 1 | 0  0  2 0  2 0 | * * * n
```

```{n} || n-cu   → height = ???

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