Acronym hinsc
Name demipenteractic scalene,
demipenteractic-pyramid pyramid,
line atop fully orthogonal demipenteract
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art
o   
    		where:
   N		o = o3o3o *b3o3o  (pt)
    		N = x3o3o *b3o3o  (hin)
o   
Confer
uniform variant:
naq  
general polytopal classes:
segmentoexa  

Incidence matrix according to Dynkin symbol

xo ox3oo3oo *c3oo3oo&#x   → height = 1/sqrt(8) = 0.353553
(line || perp hin)

o. o.3o.3o. *c3o.3o.    | 2  *  1 16  0 | 16  80   0 | 80 160  0  0 | 160 40  80  0  0 | 40 80 10 16 0 | 10 16 1
.o .o3.o3.o *c3.o3.o    | * 16  0  2 10 |  1  20  30 | 10  60 10 20 |  30 20  40  5  5 | 10 20 10 10 1 |  5  5 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
x. .. .. ..    .. ..    | 2  0 | 1  *  *  16   0   0 | 80   0  0  0 | 160  0   0  0  0 | 40 80  0  0 0 | 10 16 0
oo oo3oo3oo *c3oo3oo&#x | 1  1 | * 32  *   1  10   0 | 10  30  0  0 |  30 10  20  0  0 | 10 20  5  5 0 |  5  5 1
.. .x .. ..    .. ..    | 0  2 | *  * 80   0   2   6 |  1  12  3  6 |   6  6  12  3  2 |  3  6  6  4 1 |  3  2 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo .. .. ..    .. ..&#x | 2  1 | 1  2  0 | 16   *   *  10   0  0  0 |  30  0   0  0  0 | 10 20  0  0 0 |  5  5 0
.. ox .. ..    .. ..&#x | 1  2 | 0  2  1 |  * 160   *   1   6  0  0 |   6  3   6  0  0 |  3  6  3  2 0 |  3  2 1
.. .x3.o ..    .. ..    | 0  3 | 0  0  3 |  *   * 160 |  0   2  1  2 |   1  2   4  2  1 |  1  2  4  2 1 |  2  1 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox .. ..    .. ..&#x  2  2 | 1  4  1 |  2   2   0 | 80   *  *  *    6  0   0  0  0 |  3  6  0  0 0 |  3  2 0
.. ox3oo ..    .. ..&#x  1  3 | 0  3  3 |  0   3   1 |  * 320  *  * |   1  1   2  0  0 |  1  2  2  1 0 |  2  1 1
.. .x3.o3.o    .. ..     0  4 | 0  0  6 |  0   0   4 |  *   * 40  * |   0  2   0  2  0 |  1  0  4  0 1 |  2  0 2
.. .x3.o .. *c3.o ..     0  4 | 0  0  6 |  0   0   4 |  *   *  * 80 |   0  0   2  1  1 |  0  1  2  2 1 |  1  1 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox3oo ..    .. ..&#x  2  3 | 1  6  3 |  3   6   1 |  3   2  0  0 | 160  *   *  *  * |  1  2  0  0 0 |  2  1 0
.. ox3oo3oo    .. ..&#x  1  4 | 0  4  6 |  0   6   4 |  0   4  1  0 |   * 80   *  *  * |  1  0  2  0 0 |  2  0 1
.. ox3oo .. *c3oo ..&#x  1  4 | 0  4  6 |  0   6   4 |  0   4  0  1 |   *  * 160  *  * |  0  1  1  1 0 |  1  1 1
.. .x3.o3.o *c3.o ..     0  8 | 0  0 24 |  0   0  32 |  0   0  8  8 |   *  *   * 10  * |  0  0  2  0 1 |  1  0 2
.. .x3.o .. *c3.o3.o     0  5 | 0  0 10 |  0   0  10 |  0   0  0  5 |   *  *   *  * 16 |  0  0  0  2 1 |  0  1 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox3oo3oo    .. ..&#x  2  4 | 1  8  6 |  4  12   4 |  6   8  1  0 |   4  2   0  0  0 | 40  *  *  * * |  2  0 0
xo ox3oo .. *c3oo ..&#x  2  4 | 1  8  6 |  4  12   4 |  6   8  0  1 |   4  0   2  0  0 |  * 80  *  * * |  1  1 0
.. ox3oo3oo *c3oo ..&#x  1  8 | 0  8 24 |  0  24  32 |  0  32  8  8 |   0  8   8  1  0 |  *  * 20  * * |  1  0 1
.. ox3oo .. *c3oo3oo&#x  1  5 | 0  5 10 |  0  10  10 |  0  10  0  5 |   0  0   5  0  1 |  *  *  * 32 * |  0  1 1
.. .x3.o3.o *c3.o3.o     0 16 | 0  0 80 |  0   0 160 |  0   0 40 80 |   0  0   0 10 16 |  *  *  *  * 1 |  0  0 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox3oo3oo *c3oo ..&#x  2  8 | 1 16 24 |  8  48  32 | 24  64  8  8 |  32 16  16  1  0 |  8  8  2  0 0 | 10  * *
xo ox3oo .. *c3oo3oo&#x  2  5 | 1 10 10 |  5  20  10 | 10  20  0  5 |  10  0  10  0  1 |  0  5  0  2 0 |  * 16 *
.. ox3oo3oo *c3oo3oo&#x  1 16 | 0 16 80 |  0  80 160 |  0 160 40 80 |   0 40  80 10 16 |  0  0 10 16 1 |  *  * 2

xoo oxo oox oxo3ooo3oox&#x   → height = 1/sqrt(8) = 0.353553
(line || tegum sum of 2 gyrated and lacings-orthogonal tepes)

o.. o.. o.. o..3o..3o..      | 2  *  1 16 0  0  0 | 16  8 24 48  0  0  0 | 8 24 16 48 48  96 0  0  0  0  0 | 16 4 48 96 12 48 32 24 0  0 0 | 4 12 48 32 24  6 16 4 0 | 6 16 4 1
.o. .o. .o. .o.3.o.3.o.    & | * 16  0  2 1  3  6 |  1  2  6 12  3  9 18 | 1  3  6  6 18  36 1  3 12  8  6 |  3 2  9 18  6 24 16 12 3  5 2 | 1  3 12  8  6  6 10 4 1 | 3  5 2 2
-----------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+---------
x.. ... ... ... ... ...      | 2  0 | 1  * *  *  *  16  0  0  0  0  0  0 | 8 24  0 48  0   0 0  0  0  0  0 | 16 0 48 96  0  0  0  0 0  0 0 | 4 12 48 32 24  0  0 0 0 | 6 16 4 0
oo. oo. oo. oo.3oo.3oo.&#x & | 1  1 | * 32 *  *  *   1  1  3  6  0  0  0 | 1  3  3  6  9  18 0  0  0  0  0 |  3 1  9 18  3 12  8  6 0  0 0 | 1  3 12  8  6  3  5 2 0 | 3  5 2 1
... .x. ... ... ... ...    & | 0  2 | *  * 8  *  *   0  2  0  0  0  6  0 | 1  0  0  0 12   0 0  3  6  0  0 |  0 0  6  0  6 12  0  0 3  2 0 | 0  3  6  0  0  6  4 0 1 | 3  2 0 2
... ... ... .x. ... ...    & | 0  2 | *  * * 24  *   0  0  2  0  2  0  4 | 0  1  4  0  0   8 1  0  2  4  2 |  2 2  0  4  0  4  8  4 1  2 2 | 1  0  2  4  2  2  4 4 1 | 1  2 2 2
.oo .oo .oo .oo3.oo3.oo&#x   | 0  2 | *  * *  * 48   0  0  0  2  0  2  4 | 0  0  0  1  4   8 0  1  4  2  2 |  0 0  2  4  2  8  4  4 2  2 1 | 0  1  4  2  2  4  4 2 1 | 2  2 1 2
-----------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+---------
xo. ... ... ... ... ...&#x & | 2  1 | 1  2 0  0  0 | 16  *  *  *  *  *  *  1  3  0  6  0   0 0  0  0  0  0 |  3 0  9 18  0  0  0  0 0  0 0 | 1  3 12  8  6  0  0 0 0 | 3  5 2 0
... ox. ... ... ... ...&#x & | 1  2 | 0  2 1  0  0 |  * 16  *  *  *  *  *  1  0  0  0  6   0 0  0  0  0  0 |  0 0  6  0  3  6  0  0 0  0 0 | 0  3  6  0  0  3  2 0 0 | 3  2 0 1
... ... ... ox. ... ...&#x & | 1  2 | 0  2 0  1  0 |  *  * 48  *  *  *  *  0  1  2  0  0   4 0  0  0  0  0 |  2 1  0  4  0  2  4  2 0  0 0 | 1  0  2  4  2  1  2 2 0 | 1  2 2 1
ooo ooo ooo ooo3ooo3ooo&#x   | 1  2 | 0  2 0  0  1 |  *  *  * 96  *  *  *  0  0  0  1  2   4 0  0  0  0  0 |  0 0  2  4  1  4  2  2 0  0 0 | 0  1  4  2  2  2  2 1 0 | 2  2 1 1
... ... ... .x.3.o. ...    & | 0  3 | 0  0 0  3  0 |  *  *  *  * 16  *  * | 0  0  2  0  0   0 1  0  0  2  0 |  1 2  0  0  0  0  4  0 0  1 2 | 1  0  0  2  0  0  2 4 1 | 0  1 2 2
... .xo ... ... ... ...&#x & | 0  3 | 0  0 1  0  2 |  *  *  *  *  * 48  * | 0  0  0  0  2   0 0  1  2  0  0 |  0 0  1  0  2  4  0  0 2  1 0 | 0  1  2  0  0  4  2 0 1 | 2  1 0 2
... ... ... .xo ... ...&#x & | 0  3 | 0  0 0  1  2 |  *  *  *  *  *  * 96 | 0  0  0  0  0   2 0  0  1  1  1 |  0 0  0  1  0  2  2  2 1  1 1 | 0  0  1  1  1  2  2 2 1 | 1  1 1 2
-----------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+---------
xo. ox. ... ... ... ...&#x &  2  2 | 1  4 1  0  0 |  2  2  0  0  0  0  0 | 8  *  *  *  *   * *  *  *  *  *   0 0  6  0  0  0  0  0 0  0 0 | 0  3  6  0  0  0  0 0 0 | 3  2 0 0
xo. ... ... ox. ... ...&#x &  2  2 | 1  4 0  1  0 |  2  0  2  0  0  0  0 | * 24  *  *  *   * *  *  *  *  *   2 0  0  4  0  0  0  0 0  0 0 | 1  0  2  4  2  0  0 0 0 | 1  2 2 0
... ... ... ox.3oo. ...&#x &  1  3 | 0  3 0  3  0 |  0  0  3  0  1  0  0 | *  * 32  *  *   * *  *  *  *  * |  1 1  0  0  0  0  2  0 0  0 0 | 1  0  0  2  0  0  1 2 0 | 0  1 2 1
xoo ... ... ... ... ...&#x &  2  2 | 1  4 0  0  1 |  2  0  0  2  0  0  0 | *  *  * 48  *   * *  *  *  *  *   0 0  2  4  0  0  0  0 0  0 0 | 0  1  4  2  2  0  0 0 0 | 2  2 1 0
... oxo ... ... ... ...&#x &  1  3 | 0  3 1  0  2 |  0  1  0  2  0  1  0 | *  *  *  * 96   * *  *  *  *  * |  0 0  1  0  1  2  0  0 0  0 0 | 0  1  2  0  0  2  1 0 0 | 2  1 0 1
... ... ... oxo ... ...&#x &  1  3 | 0  3 0  1  2 |  0  0  1  2  0  0  1 | *  *  *  *  * 192 *  *  *  *  * |  0 0  0  1  0  1  1  1 0  0 0 | 0  0  1  1  1  1  1 1 0 | 1  1 1 1
... ... ... .x.3.o.3.o.    &  0  4 | 0  0 0  6  0 |  0  0  0  0  4  0  0 | *  *  *  *  *   * 4  *  *  *  * |  0 2  0  0  0  0  0  0 0  0 2 | 1  0  0  0  0  0  0 4 1 | 0  0 2 2
... .xo .ox ... ... ...&#x    0  4 | 0  0 2  0  4 |  0  0  0  0  0  4  0 | *  *  *  *  *   * * 12  *  *  * |  0 0  0  0  2  0  0  0 2  0 0 | 0  1  0  0  0  4  0 0 1 | 2  0 0 2
... .xo ... ... ... .ox&#x &  0  4 | 0  0 1  1  4 |  0  0  0  0  0  2  2 | *  *  *  *  *   * *  * 48  *  * |  0 0  0  0  0  2  0  0 1  1 0 | 0  0  1  0  0  2  2 0 1 | 1  1 0 2
... ... ... .xo3.oo ...&#x &  0  4 | 0  0 0  3  3 |  0  0  0  0  1  0  3 | *  *  *  *  *   * *  *  * 32  * |  0 0  0  0  0  0  2  0 0  1 1 | 0  0  0  1  0  0  2 2 1 | 0  1 1 2
... ... ... .xo ... .ox&#x    0  4 | 0  0 0  2  4 |  0  0  0  0  0  0  4 | *  *  *  *  *   * *  *  *  * 24 |  0 0  0  0  0  0  0  2 1  0 1 | 0  0  0  0  1  2  0 2 1 | 1  0 1 2
-----------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+---------
xo. ... ... ox.3oo. ...&#x &  2  3 | 1  6 0  3  0 |  3  0  6  0  1  0  0 | 0  3  2  0  0   0 0  0  0  0  0 | 16 *  *  *  *  *  *  * *  * * | 1  0  0  2  0  0  0 0 0 | 0  1 2 0
... ... ... ox.3oo.3oo.&#x &  1  4 | 0  4 0  6  0 |  0  0  6  0  4  0  0 | 0  0  4  0  0   0 1  0  0  0  0 |  * 8  *  *  *  *  *  * *  * * | 1  0  0  0  0  0  0 2 0 | 0  0 2 1
xoo oxo ... ... ... ...&#x &  2  3 | 1  6 1  0  2 |  3  2  0  4  0  1  0 | 1  0  0  2  2   0 0  0  0  0  0 |  * * 48  *  *  *  *  * *  * * | 0  1  2  0  0  0  0 0 0 | 2  1 0 0
xoo ... ... oxo ... ...&#x &  2  3 | 1  6 0  1  2 |  3  0  2  4  0  0  1 | 0  1  0  2  0   2 0  0  0  0  0 |  * *  * 96  *  *  *  * *  * * | 0  0  1  1  1  0  0 0 0 | 1  1 1 0
... oxo oox ... ... ...&#x    1  4 | 0  4 2  0  4 |  0  2  0  4  0  4  0 | 0  0  0  0  4   0 0  1  0  0  0 |  * *  *  * 24  *  *  * *  * * | 0  1  0  0  0  2  0 0 0 | 2  0 0 1
... oxo ... ... ... oox&#x &  1  4 | 0  4 1  1  4 |  0  1  1  4  0  2  2 | 0  0  0  0  2   2 0  0  1  0  0 |  * *  *  *  * 96  *  * *  * * | 0  0  1  0  0  1  1 0 0 | 1  1 0 1
... ... ... oxo3ooo ...&#x &  1  4 | 0  4 0  3  3 |  0  0  3  3  1  0  3 | 0  0  1  0  0   3 0  0  0  1  0 |  * *  *  *  *  * 64  * *  * * | 0  0  0  1  0  0  1 1 0 | 0  1 1 1
... ... ... oxo ... oox&#x    1  4 | 0  4 0  2  4 |  0  0  2  4  0  0  4 | 0  0  0  0  0   4 0  0  0  0  1 |  * *  *  *  *  *  * 48 *  * * | 0  0  0  0  1  1  0 1 0 | 1  0 1 1
... .xo .ox .xo ... .ox&#zx   0  8 | 0  0 4  4 16 |  0  0  0  0  0 16 16 | 0  0  0  0  0   0 0  4  8  0  4 |  * *  *  *  *  *  *  * 6  * * | 0  0  0  0  0  2  0 0 1 | 1  0 0 2
... .xo ... ... .oo3.ox&#x &  0  5 | 0  0 1  3  6 |  0  0  0  0  1  3  6 | 0  0  0  0  0   0 0  0  3  2  0 |  * *  *  *  *  *  *  * * 16 * | 0  0  0  0  0  0  2 0 1 | 0  1 0 2
... ... ... .xo3.oo3.ox&#x    0  8 | 0  0 0 12 12 |  0  0  0  0  8  0 24 | 0  0  0  0  0   0 2  0  0  8  6 |  * *  *  *  *  *  *  * *  * 4 | 0  0  0  0  0  0  0 2 1 | 0  0 1 2
-----------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+---------
xo. ... ... ox.3oo.3oo.&#x &  2  4 | 1  8 0  6  0 |  4  0 12  0  4  0  0 | 0  6  8  0  0   0 1  0  0  0  0 |  4 2  0  0  0  0  0  0 0  0 0 | 4  *  *  *  *  *  * * * | 0  0 2 0
xoo oxo oox ... ... ...&#x    2  4 | 1  8 2  0  4 |  4  4  0  8  0  4  0 | 2  0  0  4  8   0 0  1  0  0  0 |  0 0  4  0  2  0  0  0 0  0 0 | * 12  *  *  *  *  * * * | 2  0 0 0
xoo oxo ... ... ... oox&#x &  2  4 | 1  8 1  1  4 |  4  2  2  8  0  2  2 | 1  1  0  4  4   4 0  0  1  0  0 |  0 0  2  2  0  2  0  0 0  0 0 | *  * 48  *  *  *  * * * | 1  1 0 0
xoo ... ... oxo3ooo ...&#x &  2  4 | 1  8 0  3  3 |  4  0  6  6  1  0  3 | 0  3  2  3  0   6 0  0  0  1  0 |  1 0  0  3  0  0  2  0 0  0 0 | *  *  * 32  *  *  * * * | 0  1 1 0
xoo ... ... oxo ... oox&#x    2  4 | 1  8 0  2  4 |  4  0  4  8  0  0  4 | 0  2  0  4  0   8 0  0  0  0  1 |  0 0  0  4  0  0  0  2 0  0 0 | *  *  *  * 24  *  * * * | 1  0 1 0
... oxo oox oxo ... oox&#x    1  8 | 0  8 4  4 16 |  0  4  4 16  0 16 16 | 0  0  0  0 16  16 0  4  8  0  4 |  0 0  0  0  4  8  0  4 1  0 0 | *  *  *  *  * 12  * * * | 1  0 0 1
... oxo ... ... ooo3oox&#x &  1  5 | 0  5 1  3  6 |  0  1  3  6  1  3  6 | 0  0  1  0  3   6 0  0  3  2  0 |  0 0  0  0  0  3  2  0 0  1 0 | *  *  *  *  *  * 32 * * | 0  1 0 1
... ... ... oxo3ooo3oox&#x    1  8 | 0  8 0 12 12 |  0  0 12 12  8  0 24 | 0  0  8  0  0  24 2  0  0  8  6 |  0 2  0  0  0  0  8  6 0  0 1 | *  *  *  *  *  *  * 8 * | 0  0 1 1
... .xo .ox .xo3.oo3.ox&#zx   0 16 | 0  0 8 24 48 |  0  0  0  0 16 48 96 | 0  0  0  0  0   0 4 12 48 32 24 |  0 0  0  0  0  0  0  0 6 16 4 | *  *  *  *  *  *  * * 1 | 0  0 0 2
-----------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+---------
xoo oxo oox oxo ... oox&#x    2  8 | 1 16 4  4 16 |  8  8  8 32  0 16 16 | 4  4  0 16 32  32 0  4  8  0  4 |  0 0 16 16  8 16  0  8 1  0 0 | 0  4  8  0  4  2  0 0 0 | 6  * * *
xoo oxo ... ... ooo3oox&#x &  2  5 | 1 10 1  3  6 |  5  2  6 12  1  3  6 | 1  3  2  6  6  12 0  0  3  2  0 |  1 0  3  6  0  6  4  0 0  1 0 | 0  0  3  2  0  0  2 0 0 | * 16 * *
xoo ... ... oxo3ooo3oox&#x    2  8 | 1 16 0 12 12 |  8  0 24 24  8  0 24 | 0 12 16 12  0  48 2  0  0  8  6 |  8 4  0 24  0  0 16 12 0  0 1 | 2  0  0  8  6  0  0 2 0 | *  * 4 *
... oxo oox oxo3ooo3oox&#x    1 16 | 0 16 8 24 48 |  0  8 24 48 16 48 96 | 0  0 16  0 48  96 4 12 48 32 24 |  0 4  0  0 12 48 32 24 6 16 4 | 0  0  0  0  0  6 16 4 1 | *  * * 2

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