Acronym ...
Name xo3oo3oo3ox&#q,
longer variant of pentachoral antiprism,
vertex figure of staf
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art
 x3o3o o3o3o
            
            
            
            
o3o3o o3o3x 
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Face vector 10, 40, 80, 80, 32
Confer
uniform variant:
tac  

Incidence matrix according to Dynkin symbol

xo3oo3oo3ox&#q   → height = sqrt(7/5) = 1.183216
(pen || dual pen – with q-lacings)

o.3o.3o.3o.    | 5 *   4  4  0 |  6 12  6  0 | 4 12 12  4 0 | 1 4  6  4 1 0
.o3.o3.o3.o    | * 5   0  4  4 |  0  6 12  6 | 0  4 12 12 4 | 0 1  4  6 4 1
---------------+-----+----------+-------------+--------------+--------------
x. .. .. ..    | 2 0 | 10  *  * |  3  3  0  0 | 3  6  3  0 0 | 1 3  3  1 0 0
oo3oo3oo3oo&#q | 1 1 |  * 20  * |  0  3  3  0 | 0  3  6  3 0 | 0 1  3  3 1 0
.. .. .. .x    | 0 2 |  *  * 10 |  0  0  3  3 | 0  0  3  6 3 | 0 0  1  3 3 1
---------------+-----+----------+-------------+--------------+--------------
x.3o. .. ..    | 3 0 |  3  0  0 | 10  *  *  * | 2  2  0  0 0 | 1 2  1  0 0 0
xo .. .. ..&#q | 2 1 |  1  2  0 |  * 30  *  * | 0  2  2  0 0 | 0 1  2  1 0 0
.. .. .. ox&#q | 1 2 |  0  2  1 |  *  * 30  * | 0  0  2  2 0 | 0 0  1  2 1 0
.. .. .o3.x    | 0 3 |  0  0  3 |  *  *  * 10 | 0  0  0  2 2 | 0 0  0  1 2 1
---------------+-----+----------+-------------+--------------+--------------
x.3o.3o. ..     4 0 |  6  0  0 |  4  0  0  0 | 5  *  *  * * | 1 1  0  0 0 0
xo3oo .. ..&#q  3 1 |  3  3  0 |  1  3  0  0 | * 20  *  * * | 0 1  1  0 0 0
xo .. .. ox&#q  2 2 |  1  4  1 |  0  2  2  0 | *  * 30  * * | 0 0  1  1 0 0
.. .. oo3ox&#q  1 3 |  0  3  3 |  0  0  3  1 | *  *  * 20 * | 0 0  0  1 1 0
.. .o3.o3.x     0 4 |  0  0  6 |  0  0  0  4 | *  *  *  * 5 | 0 0  0  0 1 1
---------------+-----+----------+-------------+--------------+--------------
x.3o.3o.3o.     5 0 | 10  0  0 | 10  0  0  0 | 5  0  0  0 0 | 1 *  *  * * *
xo3oo3oo ..&#q  4 1 |  6  4  0 |  4  6  0  0 | 1  4  0  0 0 | * 5  *  * * *
xo3oo .. ox&#q  3 2 |  3  6  1 |  1  6  3  0 | 0  2  3  0 0 | * * 10  * * *
xo .. oo3ox&#q  2 3 |  1  6  3 |  0  3  6  1 | 0  0  3  2 0 | * *  * 10 * *
.. oo3oo3ox&#q  1 4 |  0  4  6 |  0  0  6  4 | 0  0  0  4 1 | * *  *  * 5 *
.o3.o3.o3.x     0 5 |  0  0 10 |  0  0  0 10 | 0  0  0  0 5 | * *  *  * * 1
or
o.3o.3o.3o.    & | 10   4  4 |  6 18 |  4 16 12 | 1  5 10
-----------------+----+-------+-------+----------+--------
x. .. .. ..    & |  2 | 20  * |  3  3 |  3  6  3 | 1  3  4
oo3oo3oo3oo&#q   |  2 |  * 20 |  0  6 |  0  6  6 | 0  2  6
-----------------+----+-------+-------+----------+--------
x.3o. .. ..    & |  3 |  3  0 | 20  * |  2  2  0 | 1  2  1
xo .. .. ..&#q & |  3 |  1  2 |  * 60 |  0  2  2 | 0  1  3
-----------------+----+-------+-------+----------+--------
x.3o.3o. ..    &   4 |  6  0 |  4  0 | 10  *  * | 1  1  0
xo3oo .. ..&#q &   4 |  3  3 |  1  3 |  * 40  * | 0  1  1
xo .. .. ox&#q     4 |  2  4 |  0  4 |  *  * 30 | 0  0  2
-----------------+----+-------+-------+----------+--------
x.3o.3o.3o.    &   5 | 10  0 | 10  0 |  5  0  0 | 2  *  *
xo3oo3oo ..&#q &   5 |  6  4 |  4  6 |  1  4  0 | * 10  *
xo3oo .. ox&#q &   5 |  4  6 |  1  9 |  0  2  3 | *  * 20

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