Acronym oaf, K-4.58 Name octagonal antifastegium,octagon - oap wedge,{8} || gyro op Segmentochoron display Circumradius sqrt[(1+2 cos(π/8)-2 cos2(π/8))/(2+4 cos(π/8)-6 cos2(π/8))] = 1.409438 Confer segmentochora family: n-af   n/d-af   general polytopal classes: segmentochora

Incidence matrix according to Dynkin symbol

```xoo8oxx&#x   → height(1,2) = height(1,3) = sqrt[(1+2*cos(π/8))/(2+2*cos(π/8))] = 0.860296
height(2,3) = 1
( {8} || (dual {8} || dual {8}) )

o.. o..    | 8 * * | 2  2  2 0 0 0 | 1 2 1 2 1  2 0 0 0 | 1 1 2 1 0
.o. .o.    | * 8 * | 0  2  0 2 1 0 | 0 1 2 0 0  2 1 2 0 | 1 0 1 2 1
..o ..o    | * * 8 | 0  0  2 0 1 2 | 0 0 0 1 2  2 0 2 1 | 0 1 1 2 1
-----------+-------+---------------+--------------------+----------
x.. ...    | 2 0 0 | 8  *  * * * * | 1 1 0 1 0  0 0 0 0 | 1 1 1 0 0
oo.8oo.&#x | 1 1 0 | * 16  * * * * | 0 1 1 0 0  1 0 0 0 | 1 0 1 1 0
o.o8o.o&#x | 1 0 1 | *  * 16 * * * | 0 0 0 1 1  1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | *  *  * 8 * * | 0 0 1 0 0  0 1 1 0 | 1 0 0 1 1
.oo8.oo&#x | 0 1 1 | *  *  * * 8 * | 0 0 0 0 0  2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | *  *  * * * 8 | 0 0 0 0 1  0 0 1 1 | 0 1 0 1 1
-----------+-------+---------------+--------------------+----------
x..8o..    | 8 0 0 | 8  0  0 0 0 0 | 1 * * * *  * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1  2  0 0 0 0 | * 8 * * *  * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0  2  0 1 0 0 | * * 8 * *  * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1  0  2 0 0 0 | * * * 8 *  * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0  0  2 0 0 1 | * * * * 8  * * * * | 0 1 0 1 0
ooo8ooo&#x | 1 1 1 | 0  1  1 0 1 0 | * * * * * 16 * * * | 0 0 1 1 0
.o.8.x.    | 0 8 0 | 0  0  0 8 0 0 | * * * * *  * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0  0  0 1 2 1 | * * * * *  * * 8 * | 0 0 0 1 1
..o6..x    | 0 0 8 | 0  0  0 0 0 8 | * * * * *  * * * 1 | 0 1 0 0 1
-----------+-------+---------------+--------------------+----------
xo.8ox.&#x ♦ 8 8 0 | 8 16  0 8 0 0 | 1 8 8 0 0  0 1 0 0 | 1 * * * *
x.o8o.x&#x ♦ 8 0 8 | 8  0 16 0 0 8 | 1 0 0 8 8  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 | * * 8 * *
... oxx&#x ♦ 1 2 2 | 0  2  2 1 2 1 | 0 0 1 0 1  2 0 1 0 | * * * 8 *
.oo8.xx&#x ♦ 0 8 8 | 0  0  0 8 8 8 | 0 0 0 0 0  0 1 8 1 | * * * * 1
```

```xo8ox ox&#x   → height = sqrt[(1+3 cos(π/8))/(4+4 cos(π/8))] = 0.700077
({8} || gyro op)

o. o. o.    | 8  * | 2  4  0 0 | 1  4  2  2 0 0 | 2 2 1 0
.o .o .o    | * 16 | 0  2  2 1 | 0  1  2  2 1 2 | 1 1 2 1
------------+------+-----------+----------------+--------
x. .. ..    | 2  0 | 8  *  * * | 1  2  0  0 0 0 | 2 1 0 0
oo8oo oo&#x | 1  1 | * 32  * * | 0  1  1  1 0 0 | 1 1 1 0
.. .x ..    | 0  2 | *  * 16 * | 0  0  1  0 1 1 | 1 0 1 1
.. .. .x    | 0  2 | *  *  * 8 | 0  0  0  2 0 2 | 0 1 2 1
------------+------+-----------+----------------+--------
x.8o. ..    | 8  0 | 8  0  0 0 | 1  *  *  * * * | 2 0 0 0
xo .. ..&#x | 2  1 | 1  2  0 0 | * 16  *  * * * | 1 1 0 0
.. ox ..&#x | 1  2 | 0  2  1 0 | *  * 16  * * * | 1 0 1 0
.. .. ox&#x | 1  2 | 0  2  0 1 | *  *  * 16 * * | 0 1 1 0
.o8.x ..    | 0  8 | 0  0  8 0 | *  *  *  * 2 * | 1 0 0 1
.. .x .x    | 0  4 | 0  0  2 2 | *  *  *  * * 8 | 0 0 1 1
------------+------+-----------+----------------+--------
xo8ox ..&#x ♦ 8  8 | 8 16  8 0 | 1  8  8  0 1 0 | 2 * * *
xo .. ox&#x ♦ 2  2 | 1  4  0 1 | 0  2  0  2 0 0 | * 8 * *
.. ox ox&#x ♦ 1  4 | 0  4  2 2 | 0  0  2  2 0 1 | * * 8 *
.o8.x .x    ♦ 0 16 | 0  0 16 8 | 0  0  0  0 2 8 | * * * 1

snubbed forms: xo8os2os
```

```{8} || oap   → height = sqrt[(1+3 cos(π/8))/(2+4 cos(π/8))] = 0.813764

o.. o..    | 8 * * | 2  2  2 0 0 0 | 1 2 1 2 1  2 0 0 0 | 1 1 2 1 0
.o. .o.    | * 8 * | 0  2  0 2 1 0 | 0 1 2 0 0  2 1 2 0 | 1 0 1 2 1
..o ..o    | * * 8 | 0  0  2 0 1 2 | 0 0 0 1 2  2 0 2 1 | 0 1 1 2 1
-----------+-------+---------------+--------------------+----------
x.. ...    | 2 0 0 | 8  *  * * * * | 1 1 0 1 0  0 0 0 0 | 1 1 1 0 0
oo.8oo.&#x | 1 1 0 | * 16  * * * * | 0 1 1 0 0  1 0 0 0 | 1 0 1 1 0
o.o8o.o&#x | 1 0 1 | *  * 16 * * * | 0 0 0 1 1  1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | *  *  * 8 * * | 0 0 1 0 0  0 1 1 0 | 1 0 0 1 1
.oo8.oo&#x | 0 1 1 | *  *  * * 8 * | 0 0 0 0 0  2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | *  *  * * * 8 | 0 0 0 0 1  0 0 1 1 | 0 1 0 1 1
-----------+-------+---------------+--------------------+----------
x..8o..    | 8 0 0 | 8  0  0 0 0 0 | 1 * * * *  * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1  2  0 0 0 0 | * 8 * * *  * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0  2  0 1 0 0 | * * 8 * *  * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1  0  2 0 0 0 | * * * 8 *  * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0  0  2 0 0 1 | * * * * 8  * * * * | 0 1 0 1 0
ooo8ooo&#x | 1 1 1 | 0  1  1 0 1 0 | * * * * * 16 * * * | 0 0 1 1 0
.o.8.x.    | 0 8 0 | 0  0  0 8 0 0 | * * * * *  * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0  0  0 1 2 1 | * * * * *  * * 8 * | 0 0 0 1 1
..o8..x    | 0 0 8 | 0  0  0 0 0 8 | * * * * *  * * * 1 | 0 1 0 0 1
-----------+-------+---------------+--------------------+----------
xo.8ox.&#x ♦ 8 8 0 | 8 16  0 8 0 0 | 1 8 8 0 0  0 1 0 0 | 1 * * * *
x.o8o.x&#x ♦ 8 0 8 | 8  0 16 0 0 8 | 1 0 0 8 8  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 | * * 8 * *
... oxx&#x ♦ 1 2 2 | 0  2  2 1 2 1 | 0 0 1 0 1  2 0 1 0 | * * * 8 *
.oo8.xx&#x ♦ 0 8 8 | 0  0  0 8 8 8 | 0 0 0 0 0  0 1 8 1 | * * * * 1
```