Acronym ogdow
Name octagrammic disphenoid,
octagram atop fully orthogonal octagram
Circumradius sqrt[3-sqrt(2)]/2 = 0.629640
Dual (selfdual)
Face vector 16, 80, 130, 80, 16
Confer
more general:
{n/d} || perp {n/d}  
general polytopal classes:
segmentotera   scaliform   noble  

Incidence matrix according to Dynkin symbol

xo8/3oo ox8/3oo&#x   → height = sqrt[sqrt(2)-1] = 0.643594
(pyramid product of 2 octagrams)

o.8/3o. o.8/3o.    & | 16   2  8 | 1  24 |  9 16 | 10
---------------------+----+-------+-------+-------+---
x.   .. ..   ..    & |  2 | 16  *  1   8 |  8  8 |  9
oo8/3oo oo8/3oo&#x   |  2 |  * 64 | 0   4 |  2  4 |  4
---------------------+----+-------+-------+-------+---
x.8/3o. ..   ..    & |  8 |  8  0 | 2   * |  8  0 |  8  {8/3}
xo   .. ..   ..&#x & |  3 |  1  2 | * 128 |  1  2 |  3
---------------------+----+-------+-------+-------+---
xo8/3oo ..   ..&#x &   9 |  8  8 | 1   8 | 16  * |  2
xo   .. ox   ..&#x     4 |  2  4 | 0   4 |  * 64 |  2
---------------------+----+-------+-------+-------+---
xo8/3oo ox   ..&#x &  10 |  9 16 | 1  24 |  2  8 | 16

xo4/3xo ox4/3ox&#x   → height = sqrt[sqrt(2)-1] = 0.643594
(pyramid product of 2 octagrams)

o.4/3o. o.4/3o.    | 8 *  1 1  8 0 0 | 1  8  8  4  4 0 | 8  4  4  4  4 1 | 4 4 1 1
.o4/3.o .o4/3.o    | * 8  0 0  8 1 1 | 0  4  4  8  8 1 | 1  4  4  4  4 8 | 1 1 4 4
-------------------+-----+------------+-----------------+-----------------+--------
x.   .. ..   ..    | 2 0 | 4 *  * * *  1  8  0  0  0 0 | 8  4  4  0  0 0 | 4 4 1 0
..   x. ..   ..    | 2 0 | * 4  * * *  1  0  8  0  0 0 | 8  0  0  4  4 0 | 4 4 0 1
oo4/3oo oo4/3oo&#x | 1 1 | * * 64 * * | 0  1  1  1  1 0 | 1  1  1  1  1 1 | 1 1 1 1
..   .. .x   ..    | 0 2 | * *  * 4 *  0  0  0  8  0 1 | 0  4  0  4  0 8 | 1 0 4 4
..   .. ..   .x    | 0 2 | * *  * * 4  0  0  0  0  8 1 | 0  0  4  0  4 8 | 0 1 4 4
-------------------+-----+------------+-----------------+-----------------+--------
x.4/3x. ..   ..    | 8 0 | 4 4  0 0 0 | 1  *  *  *  * * | 8  0  0  0  0 0 | 4 4 0 0  {8/3}
xo   .. ..   ..&#x | 2 1 | 1 0  2 0 0 | * 32  *  *  * * | 1  1  1  0  0 0 | 1 1 1 0
..   xo ..   ..&#x | 2 1 | 0 1  2 0 0 | *  * 32  *  * * | 1  0  0  1  1 0 | 1 1 0 1
..   .. ox   ..&#x | 1 2 | 0 0  2 1 0 | *  *  * 32  * * | 0  1  0  1  0 1 | 1 0 1 1
..   .. ..   ox&#x | 1 2 | 0 0  2 0 1 | *  *  *  * 32 * | 0  0  1  0  1 1 | 0 1 1 1
..   .. .x4/3.x    | 0 8 | 0 0  0 4 4 | *  *  *  *  * 1 | 0  0  0  0  0 8 | 0 0 4 4  {8/3}
-------------------+-----+------------+-----------------+-----------------+--------
xo4/3xo ..   ..&#x  8 1 | 4 4  8 0 0 | 1  4  4  0  0 0 | 8  *  *  *  * * | 1 1 0 0
xo   .. ox   ..&#x  2 2 | 1 0  4 1 0 | 0  2  0  2  0 0 | * 16  *  *  * * | 1 0 1 0
xo   .. ..   ox&#x  2 2 | 1 0  4 0 1 | 0  2  0  0  2 0 | *  * 16  *  * * | 0 1 1 0
..   xo ox   ..&#x  2 2 | 0 1  4 1 0 | 0  0  2  2  0 0 | *  *  * 16  * * | 1 0 0 1
..   xo ..   ox&#x  2 2 | 0 1  4 0 1 | 0  0  2  0  2 0 | *  *  *  * 16 * | 0 1 0 1
..   .. ox4/3ox&#x  1 8 | 0 0  8 4 4 | 0  0  0  4  4 1 | *  *  *  *  * 8 | 0 0 1 1
-------------------+-----+------------+-----------------+-----------------+--------
xo4/3xo ox   ..&#x  8 2 | 4 4 16 1 0 | 1  8  8  8  0 0 | 2  4  0  4  0 0 | 4 * * *
xo4/3xo ..   ox&#x  8 2 | 4 4 16 0 1 | 1  8  8  0  8 0 | 2  0  4  0  4 0 | * 4 * *
xo   .. ox4/3ox&#x  2 8 | 1 0 16 4 4 | 0  8  0  8  8 1 | 0  4  4  0  0 2 | * * 4 *
..   xo ox4/3ox&#x  2 8 | 0 1 16 4 4 | 0  0  8  8  8 1 | 0  0  0  4  4 2 | * * * 4

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