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 |
Face vector | 24, 64, 59, 19 |
Confer |
|
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
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