Acronym n/d-cuf Name n/d-grammal cupofastegium,2n-gon - n/d-prismatic wedge,n/d-grammal orthobicupolaic ring,{2n/d} || n/d-prism,{n/d} || n/d-cupola Segmentochoron display Circumradius sqrt[(5+2 cos(π d/n)-4cos2(π d/n))/(8-12 cos2(π d/n))] Lace cityin approx. ASCII-art ``` x-n/d-x x-n/d-o x-n/d-o ``` Especially {2n} || n-p (d=1)   {4} || ortho {4} (n=2,d=1)*   {6} || trip (n=3,d=1)   {8} || cube (n=4,d=1)   {10} || pip (n=5,d=1)

* The case n=2,d=1 equally would be considerable here by concept, it just has a different incidence matrix as the n/d-grams become degenerate.

Incidence matrix according to Dynkin symbol

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

o.-n/d-o. o.    | 2n  * |  2 1  2 0 0 | 1 2  2  1  2 0 | 1 1 2 1
.o-n/d-.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/d-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/d-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/d-.x ..    |  0 2n |  0 0  0 n n | * *  *  *  * 1 | 0 2 0 0
----------------+-------+-------------+----------------+--------
x.-n/d-o. x.    ♦ 2n  0 | 2n n  0 0 0 | 2 n  0  0  0 0 | 1 * * *
xx-n/d-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/d-oxo&#x   → height(1,2) = height(2,3) = sqrt[4 - 1/sin2(π d/n)]/2
height(1,3) = 1

o..-n/d-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/d-.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/d-..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/d-oo.&#x | 1  1 0 | * 2n * * *  * * | 0 1 1 0  1 0 0 0 0 | 1 0 1 1 0
o.o-n/d-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/d-.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/d-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/d-ooo&#x | 1  1 1 | 0  1 1 0 0  1 0 | * * * * 2n * * * * | 0 0 1 1 0
.x.-n/d-.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/d-..o    | 0  0 n | 0  0 0 0 0  0 n | * * * *  * * * * 1 | 0 1 0 0 1
---------------+--------+-----------------+--------------------+----------
xx.-n/d-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/d-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/d-.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/d-o..     & | 2n  * |  2  2 1 0 0 | 1  2  1 2  2 0 | 1 1 2 1
.o.-n/d-.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/d-oo.&#x  & |  1  1 |  * 4n * * * | 0  1  1 0  1 0 | 1 0 1 1
o.o-n/d-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/d-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/d-ooo&#x    |  2  1 |  0  2 1 0 0 | *  *  * * 2n * | 0 0 1 1
.x.-n/d-.x.       |  0 2n |  0  0 0 n n | *  *  * *  * 1 | 2 0 0 0
------------------+-------+-------------+----------------+--------
xx.-n/d-ox.&#x  & ♦  n 2n |  n 2n 0 n n | 1  n  n 0  0 1 | 2 * * *
x.x-n/d-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/d} || n/d-cu   → height = ???

o..-n/d-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/d-.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/d-..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/d-oo.&#x | 1  1 0 | * 2n * * *  * * | 0 1 1 0  1 0 0 0 0 | 1 0 1 1 0
o.o-n/d-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/d-.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/d-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/d-ooo&#x | 1  1 1 | 0  1 1 0 0  1 0 | * * * * 2n * * * * | 0 0 1 1 0
.x.-n/d-.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/d-..o    | 0  0 n | 0  0 0 0 0  0 n | * * * *  * * * * 1 | 0 1 0 0 1
---------------+--------+-----------------+--------------------+----------
xx.-n/d-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/d-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/d-.oo&#x ♦ 0 2n n | 0  0 0 n n 2n n | 0 0 0 0  0 1 n n 1 | * * * * 1
```