Acronym n-af, K-4.174 Name n-gonal antifastegium,n-gonal - n-antiprismatic wedge,{n} || gyro n-prism Segmentochoron display Circumradius sqrt[(1+2 cos(π/n)-2 cos2(π/n))/(2+4 cos(π/n)-6 cos2(π/n))] Confer more general: n/d-af   general polytopal classes: segmentochora Especially squasc (n=2)   traf (n=3)   squaf (n=4)   paf (n=5)   haf (n=6)   oaf (n=8)   daf (n=10)

Incidence matrix according to Dynkin symbol

```xoo-n-oxx&#x   → height(1,2) = height(1,3) = sqrt[(1+2 cos(π/n))/(2+2 cos(π/n))]
height(2,3) = 1
( {n} || (dual {n} || dual {n}) )

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

```xo-n-ox ox&#x   → height = sqrt[(1+3 cos(π/n))/(4+4 cos(π/n))]
({n} || gyro n-p)

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

snubbed forms: xo-2m-os-2-os&#x
```

```{n} || n-ap   → height = sqrt[(1+3 cos(π/n))/(2+4 cos(π/n))]

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

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