Acronym pabdihax (alt.: rixalrix)
Name parabidiminished demihexeract,
rectified hexateron atop inverted rectified hexateron
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art
               _ +--	o3o3x3o3o (dot)
           _ -

p      r 	-- o3x3o3o3o (rix)
         
 R      P	-- o3o3o3x3o (inv rix)

   \      \
    \      +--	xo3oo3ox3oo&#x (dihin)
     +--------	oo3xo3oo3ox&#x (inv dihin)

where:
p = x3o3o3o (pen)
P = o3o3o3x (dual pen)
r = o3x3o3o (rap)
R = o3o3x3o (inv rap)
Confer
uniform relative:
hax  
general polytopal classes:
segmentopeta   fundamental lace prisms   scaliform  

This scaliform polypeton is nothing but the equatorial monostratic segment of hax.


Incidence matrix according to Dynkin symbol

oo3xo3oo3ox3oo&#x   → height = 1/sqrt(3) = 0.577350
(rix || inv rix)
                 
o.3o.3o.3o.3o.     & | 30 |   8  6 |  4  12  36 |  6  8  16  16  24 |  4  2  7  20  8 | 1  6  4
---------------------+----+--------+------------+-------------------+-----------------+--------
.. x. .. .. ..     & |  2 | 120  * |  1   3   3 |  3  3   3   3   3 |  3  1  3   4  3 | 1  4  1
oo3oo3oo3oo3oo&#x    |  2 |   * 90 |  0   0   8 |  0  0   4   4   8 |  0  0  2   8  4 | 0  4  2
---------------------+----+--------+------------+-------------------+-----------------+--------
o.3x. .. .. ..     & |  3 |   3  0 | 40   *   * |  3  0   3   0   0 |  3  0  3   3  0 | 1  3  1
.. x.3o. .. ..     & |  3 |   3  0 |  * 120   * |  1  2   0   1   0 |  2  1  1   0  2 | 1  3  0
.. xo .. .. ..&#x  & |  3 |   1  2 |  *   * 360 |  0  0   1   1   2 |  0  0  1   3  2 | 0  3  1
---------------------+----+--------+------------+-------------------+-----------------+--------
o.3x.3o. .. ..     &   6 |  12  0 |  4   4   0 | 30  *   *   *   * |  2  0  1   0  0 | 1  2  0
.. x.3o.3o. ..     &   4 |   6  0 |  0   4   0 |  * 60   *   *   * |  1  1  0   0  1 | 1  2  0
oo3xo .. .. ..&#x  &   4 |   3  3 |  1   0   3 |  *  * 120   *   * |  0  0  1   2  0 | 0  2  1
.. xo3oo .. ..&#x  &   4 |   3  3 |  0   1   3 |  *  *   * 120   * |  0  0  1   0  2 | 0  3  0
.. xo .. ox ..&#x      4 |   2  4 |  0   0   4 |  *  *   *   * 180 |  0  0  0   2  1 | 0  2  1
---------------------+----+--------+------------+-------------------+-----------------+--------
o.3x.3o.3o. ..     &  10 |  30  0 | 10  20   0 |  5  5   0   0   0 | 12  *  *   *  * | 1  1  0
.. x.3o.3o.3o.     &   5 |  10  0 |  0  10   0 |  0  5   0   0   0 |  * 12  *   *  * | 1  1  0
oo3xo3oo .. ..&#x  &   7 |  12  6 |  4   4  12 |  1  0   4   4   0 |  *  * 30   *  * | 0  2  0
oo3xo .. ox ..&#x  &   5 |   4  6 |  1   0   9 |  0  0   2   0   3 |  *  *  * 120  * | 0  1  1
.. xo3oo3ox ..&#x      8 |  12 12 |  0   8  24 |  0  2   0   8   6 |  *  *  *   * 30 | 0  2  0
---------------------+----+--------+------------+-------------------+-----------------+--------
o.3x.3o.3o.3o.     &  15 |  60  0 | 20  60   0 | 15 30   0   0   0 |  6  6  0   0  0 | 2  *  *
oo3xo3oo3ox ..&#x  &  15 |  40 30 | 10  30  90 |  5 10  20  30  30 |  1  1  5  10  5 | * 12  *
oo3xo .. ox3oo&#x      6 |   6  9 |  2   0  18 |  0  0   6   0   9 |  0  0  0   6  0 | *  * 20

xooo3oxoo3ooox3ooxo&#xr   → height(1,2) = height(2,4) = height(3,4) = sqrt(3/5) = 0.774597
                            height(1,4) = height(2,3) = sqrt(2/5) = 0.632456
                          
o...3o...3o...3o...     & | 10  * |  4  4  6  0  0 |  6  4  6 12  12  12  0  0  0 |  4  6  4  6 12  4  4 12  6  12  0  0  0 | 1  4  1  4  4  1  6 12  4  4 0 | 1 1  4  5
.o..3.o..3.o..3.o..     & |  * 20 |  0  2  3  6  3 |  0  1  6  3  12  12  3  6  9 |  0  3  6  1  6  6  6  6  9  18  3  2  4 | 0  3  2  2  3  3  4  9  8  6 1 | 1 1  4  5
--------------------------+-------+----------------+------------------------------+-----------------------------------------+--------------------------------+----------
x... .... .... ....     & |  2  0 | 20  *  *  *  * |  3  1  0  3   0   0  0  0  0 |  3  3  0  3  3  0  0  3  0   0  0  0  0 | 1  3  0  3  1  0  3  3  0  0 0 | 1 1  1  3
oo..3oo..3oo..3oo..&#x  & |  1  1 |  * 40  *  *  * |  0  1  3  0   0   3  0  0  0 |  0  3  3  0  0  0  0  3  3   3  0  0  0 | 0  3  1  0  0  0  3  3  1  3 0 | 1 0  1  4
o..o3o..o3o..o3o..o&#x  & |  1  1 |  *  * 60  *  * |  0  0  0  2   4   2  0  0  0 |  0  0  0  1  4  2  2  2  1   4  0  0  0 | 0  0  0  2  2  1  1  4  2  2 0 | 0 1  2  3
.... .x.. .... ....     & |  0  2 |  *  *  * 60  * |  0  0  1  0   2   0  1  2  1 |  0  1  2  0  1  2  2  0  1   2  2  1  1 | 0  2  1  1  1  2  1  1  2  2 1 | 1 1  1  3
.o.o3.o.o3.o.o3.o.o&#x    |  0  2 |  *  *  *  * 30 |  0  0  0  0   0   4  0  0  4 |  0  0  0  0  0  0  0  2  4   8  0  0  2 | 0  0  0  0  0  0  2  4  4  4 0 | 0 0  2  4
--------------------------+-------+----------------+------------------------------+-----------------------------------------+--------------------------------+----------
x...3o... .... ....     & |  3  0 |  3  0  0  0  0 | 20  *  *  *   *   *  *  *  * |  2  1  0  1  0  0  0  0  0   0  0  0  0 | 1  2  0  2  0  0  1  0  0  0 0 | 1 1  0  2
xo.. .... .... ....&#x  & |  2  1 |  1  2  0  0  0 |  * 20  *  *   *   *  *  *  * |  0  3  0  0  0  0  0  3  0   0  0  0  0 | 0  3  0  0  0  0  3  3  0  0 0 | 1 0  1  3
.... ox.. .... ....&#x  & |  1  2 |  0  2  0  1  0 |  *  * 60  *   *   *  *  *  * |  0  1  2  0  0  0  0  0  1   0  0  0  0 | 0  2  1  0  0  0  1  0  0  2 0 | 1 0  0  3
x..o .... .... ....&#x  & |  2  1 |  1  0  2  0  0 |  *  *  * 60   *   *  *  *  * |  0  0  0  1  2  0  0  1  0   0  0  0  0 | 0  0  0  2  1  0  1  2  0  0 0 | 0 1  1  2
.... .... o..x ....&#x  & |  1  2 |  0  0  2  1  0 |  *  *  *  * 120   *  *  *  * |  0  0  0  0  1  1  1  0  0   1  0  0  0 | 0  0  0  1  1  1  0  1  1  1 0 | 0 1  1  2
oo.o3oo.o3oo.o3oo.o&#x  & |  1  2 |  0  1  1  0  1 |  *  *  *  *   * 120  *  *  * |  0  0  0  0  0  0  0  1  1   2  0  0  0 | 0  0  0  0  0  0  1  2  1  2 0 | 0 0  1  3
.o..3.x.. .... ....     & |  0  3 |  0  0  0  3  0 |  *  *  *  *   *   * 20  *  * |  0  1  0  0  0  0  2  0  0   0  2  0  1 | 0  2  0  0  1  2  1  0  2  0 1 | 1 1  1  2
.... .x..3.o.. ....     & |  0  3 |  0  0  0  3  0 |  *  *  *  *   *   *  * 40  * |  0  0  1  0  0  1  0  0  0   0  1  1  0 | 0  1  1  1  0  1  0  0  0  1 1 | 1 1  0  2
.... .x.o .... ....&#x  & |  0  3 |  0  0  0  1  2 |  *  *  *  *   *   *  *  * 60 |  0  0  0  0  0  0  0  0  1   2  0  0  1 | 0  0  0  0  0  0  1  1  2  2 0 | 0 0  1  3
--------------------------+-------+----------------+------------------------------+-----------------------------------------+--------------------------------+----------
x...3o...3o... ....     &   4  0 |  6  0  0  0  0 |  4  0  0  0   0   0  0  0  0 | 10  *  *  *  *  *  *  *  *   *  *  *  * | 1  1  0  1  0  0  0  0  0  0 0 | 1 1  0  1
xo..3ox.. .... ....&#x  &   3  3 |  3  6  0  3  0 |  1  3  3  0   0   0  1  0  0 |  * 20  *  *  *  *  *  *  *   *  *  *  * | 0  2  0  0  0  0  1  0  0  0 0 | 1 0  0  2
.... ox..3oo.. ....&#x  &   1  3 |  0  3  0  3  0 |  0  0  3  0   0   0  0  1  0 |  *  * 40  *  *  *  *  *  *   *  *  *  * | 0  1  1  0  0  0  0  0  0  1 0 | 1 0  0  2
x..o3o..o .... ....&#x  &   3  1 |  3  0  3  0  0 |  1  0  0  3   0   0  0  0  0 |  *  *  * 20  *  *  *  *  *   *  *  *  * | 0  0  0  2  0  0  1  0  0  0 0 | 0 1  0  2
x..o .... o..x ....&#x  &   2  2 |  1  0  4  1  0 |  0  0  0  2   2   0  0  0  0 |  *  *  *  * 60  *  *  *  *   *  *  *  * | 0  0  0  1  1  0  0  1  0  0 0 | 0 1  1  1
.... o..o3o..x ....&#x  &   1  3 |  0  0  3  3  0 |  0  0  0  0   3   0  0  1  0 |  *  *  *  *  * 40  *  *  *   *  *  *  * | 0  0  0  1  0  1  0  0  0  1 0 | 0 1  0  2
.... .... o..x3o..o&#x  &   1  3 |  0  0  3  3  0 |  0  0  0  0   3   0  1  0  0 |  *  *  *  *  *  * 40  *  *   *  *  *  * | 0  0  0  0  1  1  0  0  1  0 0 | 0 1  1  1
xo.o .... .... ....&#x  &   2  2 |  1  2  2  0  1 |  0  1  0  1   0   2  0  0  0 |  *  *  *  *  *  *  * 60  *   *  *  *  * | 0  0  0  0  0  0  1  2  0  0 0 | 0 0  1  2
.... ox.o .... ....&#x  &   1  3 |  0  2  1  1  2 |  0  0  1  0   0   2  0  0  1 |  *  *  *  *  *  *  *  * 60   *  *  *  * | 0  0  0  0  0  0  1  0  0  2 0 | 0 0  0  3
.... .... oo.x ....&#x  &   1  3 |  0  1  2  1  2 |  0  0  0  0   1   2  0  0  1 |  *  *  *  *  *  *  *  *  * 120  *  *  * | 0  0  0  0  0  0  0  1  1  1 0 | 0 0  1  2
.o..3.x..3.o.. ....     &   0  6 |  0  0  0 12  0 |  0  0  0  0   0   0  4  4  0 |  *  *  *  *  *  *  *  *  *   * 10  *  * | 0  1  0  0  0  1  0  0  0  0 1 | 1 1  0  1
.... .x..3.o..3.o..     &   0  4 |  0  0  0  6  0 |  0  0  0  0   0   0  0  4  0 |  *  *  *  *  *  *  *  *  *   *  * 10  * | 0  0  1  1  0  0  0  0  0  0 1 | 1 1  0  1
.o.o3.x.o .... ....&#x  &   0  4 |  0  0  0  3  3 |  0  0  0  0   0   0  1  0  3 |  *  *  *  *  *  *  *  *  *   *  *  * 20 | 0  0  0  0  0  0  1  0  2  0 0 | 0 0  1  2
--------------------------+-------+----------------+------------------------------+-----------------------------------------+--------------------------------+----------
x...3o...3o...3o...     &   5  0 | 10  0  0  0  0 | 10  0  0  0   0   0  0  0  0 |  5  0  0  0  0  0  0  0  0   0  0  0  0 | 2  *  *  *  *  *  *  *  *  * * | 1 1  0  0
xo..3ox..3oo.. ....&#x  &   4  6 |  6 12  0 12  0 |  4  6 12  0   0   0  4  4  0 |  1  4  4  0  0  0  0  0  0   0  1  0  0 | * 10  *  *  *  *  *  *  *  * * | 1 0  0  1
.... ox..3oo..3oo..&#x  &   1  4 |  0  4  0  6  0 |  0  0  6  0   0   0  0  4  0 |  0  0  4  0  0  0  0  0  0   0  0  1  0 | *  * 10  *  *  *  *  *  *  * * | 1 0  0  1
x..o3o..o3o..x ....&#x  &   4  4 |  6  0 12  6  0 |  4  0  0 12  12   0  0  4  0 |  1  0  0  4  6  4  0  0  0   0  0  1  0 | *  *  * 10  *  *  *  *  *  * * | 0 1  0  1
x..o .... o..x3o..o&#x  &   2  3 |  1  0  6  3  0 |  0  0  0  3   6   0  1  0  0 |  0  0  0  0  3  0  2  0  0   0  0  0  0 | *  *  *  * 20  *  *  *  *  * * | 0 1  1  0
.... o..o3o..x3o..o&#x  &   1  6 |  0  0  6 12  0 |  0  0  0  0  12   0  4  4  0 |  0  0  0  0  0  4  4  0  0   0  1  0  0 | *  *  *  *  * 10  *  *  *  * * | 0 1  0  1
xo.o3ox.o .... ....&#x  &   3  4 |  3  6  3  3  3 |  1  3  3  3   0   6  1  0  3 |  0  1  0  1  0  0  0  3  3   0  0  0  1 | *  *  *  *  *  * 20  *  *  * * | 0 0  0  2
xo.o .... oo.x ....&#x  &   2  3 |  1  2  4  1  2 |  0  1  0  2   2   4  0  0  1 |  0  0  0  0  1  0  0  2  0   2  0  0  0 | *  *  *  *  *  *  * 60  *  * * | 0 0  1  1
.... .... oo.x3oo.o&#x  &   1  4 |  0  1  3  3  3 |  0  0  0  0   3   3  1  0  3 |  0  0  0  0  0  0  1  0  0   3  0  0  1 | *  *  *  *  *  *  *  * 40  * * | 0 0  1  1
.... oxoo3ooox ....&#xr     2  6 |  0  6  6  6  6 |  0  0  6  0   6  12  0  2  6 |  0  0  2  0  0  2  0  0  6   6  0  0  0 | *  *  *  *  *  *  *  *  * 20 * | 0 0  0  2
.o..3.x..3.o..3.o..     &   0 10 |  0  0  0 30  0 |  0  0  0  0   0   0 10 20  0 |  0  0  0  0  0  0  0  0  0   0  5  5  0 | *  *  *  *  *  *  *  *  *  * 2 | 1 1  0  0
--------------------------+-------+----------------+------------------------------+-----------------------------------------+--------------------------------+----------
xo..3ox..3oo..3oo..&#x  &   5 10 | 10 20  0 30  0 | 10 10 30  0   0   0 10 20  0 |  5 10 20  0  0  0  0  0  0   0  5  5  0 | 1  5  5  0  0  0  0  0  0  0 1 | 2 *  *  *
x..o3o..o3o..x3o..o&#x  &   5 10 | 10  0 30 30  0 | 10  0  0 30  60   0 10 20  0 |  5  0  0 10 30 20 20  0  0   0  5  5  0 | 1  0  0  5 10  5  0  0  0  0 1 | * 2  *  *
xo.o .... oo.x3oo.o&#x  &   2  4 |  1  2  6  3  3 |  0  1  0  3   6   6  1  0  3 |  0  0  0  0  3  0  2  3  0   6  0  0  1 | 0  0  0  0  1  0  0  3  2  0 0 | * * 20  *
xooo3oxoo3ooox ....&#x  &   5 10 |  6 16 18 18 12 |  4  6 18 12  24  36  4  8 18 |  1  4  8  4  6  8  4 12 18  24  1  1  4 | 0  1  1  1  0  1  4  6  4  4 0 | * *  * 10  cycle (ABDC)

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