Acronym n-aw, {2n} || n-ap
Name anti-n-wedge,
n-gonal anti-wedge,
2n-gon - n-antiprismatic wedge,
n-gonal gyrobicupolaic ring,
{2n} || n-antiprism,
{n} || gyrated n-cupola
Segmentochoron display
Circumradius sqrt[(3-2 cos(π/n))/(5-6 cos(π/n))]
Lace city
in approx. ASCII-art
    x-n-x    
             
x-n-o   o-n-x
Confer
general polytopal classes:
segmentochora  
Especially {4} || tet (n=2)*   {6} || oct (n=3)   {8} || squap (n=4)   {10} || pap (n=5)  

* 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

xxo-n-oxx&#x   → height(1,2) = height(2,3) = sqrt(1-1/[4 sin^2(π/n)])
                 height(1,3) = sqrt[(1+2*cos(π/n))/(2+2*cos(π/n))]

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

os2xo2nos&#x   (2 < n < 5.363958)   → height = sqrt[(5-6 cos(π/n))/(8-8 cos(π/n))]
({2n} || n-ap)

      o.2o.2no.      | 2n  * |  2  2  0  0 | 1  1  2 0  2  0 | 2 0  2
demi( .o2.o2n.o    ) |  * 2n |  0  2  2  2 | 0  2  1 1  2  3 | 1 1  3
---------------------+-------+-------------+-----------------+-------
      .. x.  ..      |  2  0 | 2n  *  *  * | 1  0  1 0  1  0 | 2 0  1
demi( oo2oo2noo&#x ) |  1  1 |  * 4n  *  * | 0  1  1 0  1  0 | 1 0  2
      .s .2  .s      |  0  2 |  *  * 2n  * | 0  1  0 0  0  2 | 0 1  2
sefa( .. .o2n.s    ) |  0  2 |  *  *  * 2n | 0  0  0 1  1  1 | 1 1  1
---------------------+-------+-------------+-----------------+-------
      .. x.2no.      | 2n  0 | 2n  0  0  0 | 1  *  * *  *  * | 2 0  0
      os .2  os&#x   |  1  2 |  0  2  1  0 | * 2n  * *  *  * | 0 0  2
demi( .. xo  ..&#x ) |  2  1 |  1  2  0  0 | *  * 2n *  *  * | 1 0  1
      .. .o2n.s      |  0  n |  0  0  0  n | *  *  * 2  *  * | 1 1  0
sefa( .. xo2nos&#x ) |  2  2 |  1  2  0  1 | *  *  * * 2n  * | 1 0  1
sefa( .s2.o2n.s    ) |  0  3 |  0  0  2  1 | *  *  * *  * 2n | 0 1  1
---------------------+-------+-------------+-----------------+-------
      .. xo2nos&#x    2n  n | 2n 2n  0  n | 1  0  n 1  n  0 | 2 *  *
      .s2.o2n.s        0 2n |  0  0 2n 2n | 0  0  0 2  0 2n | * 1  *
sefa( os2xo2nos&#x )   2  3 |  1  4  2  1 | 0  2  1 0  1  1 | * * 2n

starting figure: ox xo2nox&#x

{n} || gyro n-cu   → height = ???

  n *  * | 2  2  2 0  0 0 0 | 1 2 2 1  2 1 0 0 0 0 | 1 1 2 1 0
  * n  * | 0  2  0 2  2 0 0 | 0 1 0 2  2 0 1 2 1 0 | 1 0 1 2 1
  * * 2n | 0  0  1 0  1 1 1 | 0 0 1 0  1 1 0 1 1 1 | 0 1 1 1 1
---------+------------------+----------------------+----------
  2 0  0 | n  *  * *  * * * | 1 1 1 0  0 0 0 0 0 0 | 1 1 1 0 0
  1 1  0 | * 2n  * *  * * * | 0 1 0 1  1 0 0 0 0 0 | 1 0 1 1 0
  1 0  1 | *  * 2n *  * * * | 0 0 1 0  1 1 0 0 0 0 | 0 1 1 1 0
  0 2  0 | *  *  * n  * * * | 0 0 0 1  0 0 1 1 0 0 | 1 0 0 1 1
  0 1  1 | *  *  * * 2n * * | 0 0 0 0  1 0 0 1 1 0 | 0 0 1 1 1
  0 0  2 | *  *  * *  * n * | 0 0 1 0  0 0 0 0 1 1 | 0 1 1 0 1
  0 0  2 | *  *  * *  * * n | 0 0 0 0  0 1 0 1 0 1 | 0 1 0 1 1
---------+------------------+----------------------+----------
  n 0  0 | n  0  0 0  0 0 0 | 1 * * *  * * * * * * | 1 1 0 0 0
  2 1  0 | 1  2  0 0  0 0 0 | * n * *  * * * * * * | 1 0 1 0 0
  2 0  2 | 1  0  2 0  0 1 0 | * * n *  * * * * * * | 0 1 1 0 0
  1 2  0 | 0  2  0 1  0 0 0 | * * * n  * * * * * * | 1 0 0 1 0
  1 1  1 | 0  1  1 0  1 0 0 | * * * * 2n * * * * * | 0 0 1 1 0
  1 0  2 | 0  0  2 0  0 0 1 | * * * *  * n * * * * | 0 1 0 1 0
  0 n  0 | 0  0  0 n  0 0 0 | * * * *  * * 1 * * * | 1 0 0 0 1
  0 2  2 | 0  0  0 1  2 0 1 | * * * *  * * * n * * | 0 0 0 1 1
  0 1  2 | 0  0  0 0  2 1 0 | * * * *  * * * * n * | 0 0 1 0 1
  0 0 2n | 0  0  0 0  0 n n | * * * *  * * * * * 1 | 0 1 0 0 1
---------+------------------+----------------------+----------
 n n  0 | n 2n  0 n  0 0 0 | 1 n 0 n  0 0 1 0 0 0 | 1 * * * *
 n 0 2n | n  0 2n 0  0 n n | 1 0 n 0  0 n 0 0 0 1 | * 1 * * *
 2 1  2 | 1  2  2 0  2 1 0 | 0 1 1 0  2 0 0 0 1 0 | * * n * *
 1 2  2 | 0  2  2 1  2 0 1 | 0 0 0 1  2 1 0 1 0 0 | * * * n *
 0 n 2n | 0  0  0 n 2n n n | 0 0 0 0  0 0 1 n n 1 | * * * * 1

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