Acronym he (old: ache)
Name hexadecaexon,
trirectified octaexon,
equatorial cross-section of (vertex first) 1/q-octo,
Gosset polytope 03,3
Circumradius 1
Inradius 1/sqrt(7) = 0.377964
Lace city
in approx. ASCII-art 
R   D 		-- o3o3x3o3o3o (bril)
      
 D   r		-- o3o3o3x3o3o (inv. bril)

where:
R = o3x3o3o3o (rix)
D = o3o3x3o3o (dot)
r = o3o3o3x3o (inv. rix)
Volume 151/1260 = 0.119841
Surface 151 sqrt(7)/180 = 2.219491
Dihedral angles
(at margins)
  • at dot between bril and bril:   arccos(-1/7) = 98.213211°
  • at rix between bril and bril:   arccos(1/7) = 81.786789°
Face vector 70, 560, 1120, 980, 448, 112, 16
Confer
related segmentoexa:
tetdippy   trarapdafup   tetdippa octdip  
general polytopal classes:
Wythoffian polyexa   noble polytopes   segmentoexa   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
analogs:
mid-rectified simplex mrSn  
External
links 		wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

o3o3o3x3o3o3o

. . . . . . . | 70 ♦  16 |  24  24 |  16  36  16 |  4  24  24  4 |  6 16  6 | 4 4
--------------+----+-----+---------+-------------+---------------+----------+----
. . . x . . . |  2 | 560 |   3   3 |   3   9   3 |  1   9   9  1 |  3  9  3 | 3 3
--------------+----+-----+---------+-------------+---------------+----------+----
. . o3x . . . |  3 |   3 | 560   * |   2   3   0 |  1   6   3  0 |  3  6  1 | 3 2
. . . x3o . . |  3 |   3 |   * 560 |   0   3   2 |  0   3   6  1 |  1  6  3 | 2 3
--------------+----+-----+---------+-------------+---------------+----------+----
. o3o3x . . . ♦  4 |   6 |   4   0 | 280   *   * |  1   3   0  0 |  3  3  0 | 3 1
. . o3x3o . . ♦  6 |  12 |   4   4 |   * 420   * |  0   2   2  0 |  1  4  1 | 2 2
. . . x3o3o . ♦  4 |   6 |   0   4 |   *   * 280 |  0   0   3  1 |  0  3  3 | 1 3
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x . . . ♦  5 |  10 |  10   0 |   5   0   0 | 56   *   *  * |  3  0  0 | 3 0
. o3o3x3o . . ♦ 10 |  30 |  20  10 |   5   5   0 |  * 168   *  * |  1  2  0 | 2 1
. . o3x3o3o . ♦ 10 |  30 |  10  20 |   0   5   5 |  *   * 168  * |  0  2  1 | 1 2
. . . x3o3o3o ♦  5 |  10 |   0  10 |   0   0   5 |  *   *   * 56 |  0  0  3 | 0 3
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x3o . . ♦ 15 |  60 |  60  20 |  30  15   0 |  6   6   0  0 | 28  *  * | 2 0
. o3o3x3o3o . ♦ 20 |  90 |  60  60 |  15  30  15 |  0   6   6  0 |  * 56  * | 1 1
. . o3x3o3o3o ♦ 15 |  60 |  20  60 |   0  15  30 |  0   0   6  6 |  *  * 28 | 0 2
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x3o3o . ♦ 35 | 210 | 210 140 | 105 105  35 | 21  42  21  0 |  7  7  0 | 8 *
. o3o3x3o3o3o ♦ 35 | 210 | 140 210 |  35 105 105 |  0  21  42 21 |  0  7  7 | * 8

or
. . . . . . .    | 70 ♦  16 |   48 |  32  36 |   8  48 | 12 16 |  8
-----------------+----+-----+------+---------+---------+-------+---
. . . x . . .    |  2 | 560 |    6 |   6   9 |   2  18 |  6  9 |  6
-----------------+----+-----+------+---------+---------+-------+---
. . o3x . . .  & |  3 |   3 | 1120 |   2   3 |   1   9 |  4  6 |  5
-----------------+----+-----+------+---------+---------+-------+---
. o3o3x . . .  & ♦  4 |   6 |    4 | 560   * |   1   3 |  3  3 |  4
. . o3x3o . .    ♦  6 |  12 |    8 |   * 420 |   0   4 |  2  4 |  4
-----------------+----+-----+------+---------+---------+-------+---
o3o3o3x . . .  & ♦  5 |  10 |   10 |   5   0 | 112   * |  3  0 |  3
. o3o3x3o . .  & ♦ 10 |  30 |   30 |   5   5 |   * 336 |  1  2 |  3
-----------------+----+-----+------+---------+---------+-------+---
o3o3o3x3o . .  & ♦ 15 |  60 |   80 |  30  15 |   6   6 | 56  * |  2
. o3o3x3o3o .    ♦ 20 |  90 |  120 |  30  30 |   0  12 |  * 56 |  2
-----------------+----+-----+------+---------+---------+-------+---
o3o3o3x3o3o .  & ♦ 35 | 210 |  350 | 140 105 |  21  63 |  7  7 | 16


oo3oo3xo3ox3oo3oo&#x   → height = 2/sqrt(7) = 0.755929
(bril || inv bril)

o.3o.3o.3o.3o.3o.    | 35  * ♦  12   4   0 |  12  18  12   6   0   0 |  4  18  12  12  18   4   0   0  0 |  6 12  3  4  18  12  1  0  0  0 | 4 3  6 12  3 0 0 | 1 4 3 0
.o3.o3.o3.o3.o3.o    |  * 35 ♦   0   4  12 |   0   0   6  12  18  12 |  0   0   0   4  18  12  12  18  4 |  0  0  0  1  12  18  4  3 12  6 | 0 0  3 12  6 3 4 | 0 3 4 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
.. .. x. .. .. ..    |  2  0 | 210   *   * |   2   3   1   0   0   0 |  1   6   3   2   3   0   0   0  0 |  3  6  1  1   6   3  0  0  0  0 | 3 2  3  6  1 0 0 | 1 3 2 0
oo3oo3oo3oo3oo3oo&#x |  1  1 |   * 140   * |   0   0   3   3   0   0 |  0   0   0   3   9   3   0   0  0 |  0  0  0  1   9   9  1  0  0  0 | 0 0  3  9  3 0 0 | 0 3 3 0
.. .. .. .x .. ..    |  0  2 |   *   * 210 |   0   0   0   1   3   2 |  0   0   0   0   3   2   3   6  1 |  0  0  0  0   3   6  1  1  6  3 | 0 0  1  6  3 2 3 | 0 2 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
.. o.3x. .. .. ..    |  3  0 |   3   0   0 | 140   *   *   *   *   * |  1   3   0   1   0   0   0   0  0 |  3  3  0  1   3   0  0  0  0  0 | 3 1  3  3  0 0 0 | 1 3 1 0
.. .. x.3o. .. ..    |  3  0 |   3   0   0 |   * 210   *   *   *   * |  0   2   2   0   1   0   0   0  0 |  1  4  1  0   2   2  0  0  0  0 | 2 2  1  4  1 0 0 | 1 2 2 0
.. .. xo .. .. ..&#x |  2  1 |   1   2   0 |   *   * 210   *   *   * |  0   0   0   2   3   0   0   0  0 |  0  0  0  1   6   3  0  0  0  0 | 0 0  3  6  1 0 0 | 0 3 2 0
.. .. .. ox .. ..&#x |  1  2 |   0   2   1 |   *   *   * 210   *   * |  0   0   0   0   3   2   0   0  0 |  0  0  0  0   3   6  1  0  0  0 | 0 0  1  6  3 0 0 | 0 2 3 0
.. .. .o3.x .. ..    |  0  3 |   0   0   3 |   *   *   *   * 210   * |  0   0   0   0   1   0   2   2  0 |  0  0  0  0   2   2  0  1  4  1 | 0 0  1  4  1 2 2 | 0 2 2 1
.. .. .. .x3.o ..    |  0  3 |   0   0   3 |   *   *   *   *   * 140 |  0   0   0   0   0   1   0   3  1 |  0  0  0  0   0   3  1  0  3  3 | 0 0  0  3  3 1 3 | 0 1 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x. .. .. ..    ♦  4  0 |   6   0   0 |   4   0   0   0   0   0 | 35   *   *   *   *   *   *   *  * |  3  0  0  1   0   0  0  0  0  0 | 3 0  3  0  0 0 0 | 1 3 0 0
.. o.3x.3o. .. ..    ♦  6  0 |  12   0   0 |   4   4   0   0   0   0 |  * 105   *   *   *   *   *   *  * |  1  2  0  0   1   0  0  0  0  0 | 2 1  1  2  0 0 0 | 1 2 1 0
.. .. x.3o.3o. ..    ♦  4  0 |   6   0   0 |   0   4   0   0   0   0 |  *   * 105   *   *   *   *   *  * |  0  2  1  0   1   0  0  0  0  0 | 1 2  0  2  1 0 0 | 1 1 2 0
.. oo3xo .. .. ..&#x ♦  3  1 |   3   3   0 |   1   0   3   0   0   0 |  *   *   * 140   *   *   *   *  * |  0  0  0  1   3   0  0  0  0  0 | 0 0  3  3  0 0 0 | 0 3 1 0
.. .. xo3ox .. ..&#x ♦  3  3 |   3   6   3 |   0   1   3   3   1   0 |  *   *   *   * 210   *   *   *  * |  0  0  0  0   2   2  0  0  0  0 | 0 0  1  4  1 0 0 | 0 2 2 0
.. .. .. ox3oo ..&#x ♦  1  3 |   0   3   3 |   0   0   0   3   0   1 |  *   *   *   *   * 140   *   *  * |  0  0  0  0   0   3  1  0  0  0 | 0 0  0  3  3 0 0 | 0 1 3 0
.. .o3.o3.x .. ..    ♦  0  4 |   0   0   6 |   0   0   0   0   4   0 |  *   *   *   *   *   * 105   *  * |  0  0  0  0   1   0  0  1  2  0 | 0 0  1  2  0 2 1 | 0 2 1 1
.. .. .o3.x3.o ..    ♦  0  6 |   0   0  12 |   0   0   0   0   4   4 |  *   *   *   *   *   *   * 105  * |  0  0  0  0   0   1  0  0  2  1 | 0 0  0  2  1 1 2 | 0 1 2 1
.. .. .. .x3.o3.o    ♦  0  4 |   0   0   6 |   0   0   0   0   0   4 |  *   *   *   *   *   *   *   * 35 |  0  0  0  0   0   0  1  0  0  3 | 0 0  0  0  3 0 3 | 0 0 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o. .. ..    ♦ 10  0 |  30   0   0 |  20  10   0   0   0   0 |  5   5   0   0   0   0   0   0  0 | 21  *  *  *   *   *  *  *  *  * | 2 0  1  0  0 0 0 | 1 2 0 0
.. o.3x.3o.3o. ..    ♦ 10  0 |  30   0   0 |  10  20   0   0   0   0 |  0   5   5   0   0   0   0   0  0 |  * 42  *  *   *   *  *  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
.. .. x.3o.3o.3o.    ♦  5  0 |  10   0   0 |   0  10   0   0   0   0 |  0   0   5   0   0   0   0   0  0 |  *  * 21  *   *   *  *  *  *  * | 0 2  0  0  1 0 0 | 1 0 2 0
oo3oo3xo .. .. ..&#x ♦  4  1 |   6   4   0 |   4   0   6   0   0   0 |  1   0   0   4   0   0   0   0  0 |  *  *  * 35   *   *  *  *  *  * | 0 0  3  0  0 0 0 | 0 3 0 0
.. oo3xo3ox .. ..&#x ♦  6  4 |  12  12   6 |   4   4  12   6   4   0 |  0   1   0   4   4   0   1   0  0 |  *  *  *  * 105   *  *  *  *  * | 0 0  1  2  0 0 0 | 0 2 1 0
.. .. xo3ox3oo ..&#x ♦  4  6 |   6  12  12 |   0   4   6  12   4   4 |  0   0   1   0   4   4   0   1  0 |  *  *  *  *   * 105  *  *  *  * | 0 0  0  2  1 0 0 | 0 1 2 0
.. .. .. ox3oo3oo&#x ♦  1  4 |   0   4   6 |   0   0   0   6   0   4 |  0   0   0   0   0   4   0   0  1 |  *  *  *  *   *   * 35  *  *  * | 0 0  0  0  3 0 0 | 0 0 3 0
.o3.o3.o3.x .. ..    ♦  0  5 |   0   0  10 |   0   0   0   0  10   0 |  0   0   0   0   0   0   5   0  0 |  *  *  *  *   *   *  * 21  *  * | 0 0  1  0  0 2 0 | 0 2 0 1
.. .o3.o3.x3.o ..    ♦  0 10 |   0   0  30 |   0   0   0   0  20  10 |  0   0   0   0   0   0   5   5  0 |  *  *  *  *   *   *  *  * 42  * | 0 0  0  1  0 1 1 | 0 1 1 1
.. .. .o3.x3.o3.o    ♦  0 10 |   0   0  30 |   0   0   0   0  10  20 |  0   0   0   0   0   0   0   5  5 |  *  *  *  *   *   *  *  *  * 21 | 0 0  0  0  1 0 2 | 0 0 2 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o.3o. ..    ♦ 20  0 |  90   0   0 |  60  60   0   0   0   0 | 15  30  15   0   0   0   0   0  0 |  6  6  0  0   0   0  0  0  0  0 | 7 *  *  *  * * * | 1 1 0 0
.. o.3x.3o.3o.3o.    ♦ 15  0 |  60   0   0 |  20  60   0   0   0   0 |  0  15  30   0   0   0   0   0  0 |  0  6  6  0   0   0  0  0  0  0 | * 7  *  *  * * * | 1 0 1 0
oo3oo3xo3ox .. ..&#x ♦ 10  5 |  30  20  10 |  20  10  30  10  10   0 |  5   5   0  20  10   0   5   0  0 |  1  0  0  5   5   0  0  1  0  0 | * * 21  *  * * * | 0 2 0 0
.. oo3xo3ox3oo ..&#x ♦ 10 10 |  30  30  30 |  10  20  30  30  20  10 |  0   5   5  10  20  10   5   5  0 |  0  1  0  0   5   5  0  0  1  0 | * *  * 42  * * * | 0 1 1 0
.. .. xo3ox3oo3oo&#x ♦  5 10 |  10  20  30 |   0  10  10  30  10  20 |  0   0   5   0  10  20   0   5  5 |  0  0  1  0   0   5  5  0  0  1 | * *  *  * 21 * * | 0 0 2 0
.o3.o3.o3.x3.o ..    ♦  0 15 |   0   0  60 |   0   0   0   0  60  20 |  0   0   0   0   0   0  30  15  0 |  0  0  0  0   0   0  0  6  6  0 | * *  *  *  * 7 * | 0 1 0 1
.. .o3.o3.x3.o3.o    ♦  0 20 |   0   0  90 |   0   0   0   0  60  60 |  0   0   0   0   0   0  15  30 15 |  0  0  0  0   0   0  0  0  6  6 | * *  *  *  * * 7 | 0 0 1 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o.3o.3o.    ♦ 35  0 | 210   0   0 | 140 210   0   0   0   0 | 35 105 105   0   0   0   0   0  0 | 21 42 21  0   0   0  0  0  0  0 | 7 7  0  0  0 0 0 | 1 * * *
oo3oo3xo3ox3oo ..&#x ♦ 20 15 |  90  60  60 |  60  60  90  60  60  20 | 15  30  15  60  60  20  30  15  0 |  6  6  0 15  30  15  0  6  6  0 | 1 0  6  6  0 1 0 | * 7 * *
.. oo3xo3ox3oo3oo&#x ♦ 15 20 |  60  60  90 |  20  60  60  90  60  60 |  0  15  30  20  60  60  15  30 15 |  0  6  6  0  15  30 15  0  6  6 | 0 1  0  6  6 0 1 | * * 7 *
.o3.o3.o3.x3.o3.o    ♦  0 35 |   0   0 210 |   0   0   0   0 210 140 |  0   0   0   0   0   0 105 105 35 |  0  0  0  0   0   0  0 21 42 21 | 0 0  0  0  0 7 7 | * * * 1


oxoo3ooxo xooo3oxoo3ooxo3ooox&#xt   → all heights = 2/sqrt(15) = 0.516398
(pen || trarap || bi-inv trarap || dual pen)

o...3o... o...3o...3o...3o...     & | 10  * ♦  4  12  0   0   0 |  6  12 12  18  0  0   0   3   0 |  4  4 12 18  12  18  0  0  0   0   0   0 | 1  4 12  3  6 18  12 0  0  0 | 3  6 12  3  4 0 | 3  5
.o..3.o.. .o..3.o..3.o..3.o..     & |  * 60 ♦  0   2  2   6   6 |  0   4  1   6  1  3   6   9  18 |  0  2  2  3   6  15  3  2  3  12   8  12 | 0  1  3  2  9  7  18 1  5 10 | 1  4  8  7  6 2 | 3  5
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... x... .... .... ....     & |  2  0 | 20   *  *   *   * |  3   0  3   0  0  0   0   3   0 |  3  0  3  9   0   0  0  0  0   0   0   0 | 1  1  9  0  0  9   0 0  0  0 | 3  3  9  0  0 0 | 3  3
oo..3oo.. oo..3oo..3oo..3oo..&#x  & |  1  1 |  * 120  *   *   * |  0   2  1   3  0  0   0   3   0 |  0  1  2  3   3   6  0  0  0   0   0   0 | 0  1  3  1  3  6   6 0  0  0 | 1  3  6  2  3 0 | 2  4
.x.. .... .... .... .... ....     & |  0  2 |  *   * 60   *   * |  0   2  0   0  1  0   0   3   0 |  0  2  1  0   0   6  0  0  3   3   0   0 | 0  1  0  0  9  3   6 0  1  0 | 0  4  3  2  6 0 | 1  5
.... .... .... .x.. .... ....     & |  0  2 |  *   *  * 180   * |  0   0  0   1  0  1   2   0   2 |  0  0  0  1   2   2  2  1  0   1   2   4 | 0  0  2  1  1  2   6 1  1  6 | 1  1  5  4  2 2 | 3  3
.oo.3.oo. .oo.3.oo.3.oo.3.oo.&#x    |  0  2 |  *   *  *   * 180 |  0   0  0   0  0  0   0   2   4 |  0  0  0  0   0   4  0  0  1   4   2   4 | 0  0  0  0  4  2   8 0  2  4 | 0  2  4  4  4 1 | 2  4
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... x...3o... .... ....     & |  3  0 |  3   0  0   0   0 | 20   *  *   *  *  *   *   *   * |  2  0  0  3   0   0  0  0  0   0   0   0 | 1  0  6  0  0  3   0 0  0  0 | 3  1  6  0  0 0 | 3  2
ox.. .... .... .... .... ....&#x  & |  1  2 |  0   2  1   0   0 |  * 120  *   *  *  *   *   *   * |  0  1  1  0   0   3  0  0  0   0   0   0 | 0  1  0  0  3  3   3 0  0  0 | 0  3  3  1  3 0 | 1  4
.... .... xo.. .... .... ....&#x  & |  2  1 |  1   2  0   0   0 |  *   * 60   *  *  *   *   *   * |  0  0  2  3   0   0  0  0  0   0   0   0 | 0  1  3  0  0  6   0 0  0  0 | 1  3  6  0  0 0 | 2  3
.... .... .... ox.. .... ....&#x  & |  1  2 |  0   2  0   1   0 |  *   *  * 180  *  *   *   *   * |  0  0  0  1   2   2  0  0  0   0   0   0 | 0  0  2  1  1  2   4 0  0  0 | 1  1  4  1  2 0 | 2  3
.x..3.o.. .... .... .... ....     & |  0  3 |  0   0  3   0   0 |  *   *  *   * 20  *   *   *   * |  0  2  0  0   0   0  0  0  3   0   0   0 | 0  1  0  0  9  0   0 0  0  0 | 0  4  0  0  6 0 | 0  5
.... .... .o..3.x.. .... ....     & |  0  3 |  0   0  0   3   0 |  *   *  *   *  * 60   *   *   * |  0  0  0  1   0   0  2  0  0   0   2   0 | 0  0  2  0  0  2   0 1  1  4 | 1  1  4  2  0 2 | 3  2
.... .... .... .x..3.o.. ....     & |  0  3 |  0   0  0   3   0 |  *   *  *   *  *  * 120   *   * |  0  0  0  0   1   0  1  1  0   0   0   2 | 0  0  1  1  0  0   3 1  0  4 | 1  0  3  3  1 2 | 3  2
.xo. .... .... .... .... ....&#x  & |  0  3 |  0   0  1   0   2 |  *   *  *   *  *  *   * 180   * |  0  0  0  0   0   2  0  0  1   2   0   0 | 0  0  0  0  4  1   4 0  1  0 | 0  2  2  2  4 0 | 1  4
.... .... .... .xo. .... ....&#x  & |  0  3 |  0   0  0   1   2 |  *   *  *   *  *  *   *   * 360 |  0  0  0  0   0   1  0  0  0   1   1   2 | 0  0  0  0  1  1   4 0  1  3 | 0  1  3  3  2 1 | 2  3
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... x...3o...3o... ....     & ♦  4  0 |  6   0  0   0   0 |  4   0  0   0  0  0   0   0   0 | 10  *  *  *   *   *  *  *  *   *   *   * | 1  0  3  0  0  0   0 0  0  0 | 3  0  3  0  0 0 | 3  1
ox..3oo.. .... .... .... ....&#x  & ♦  1  3 |  0   3  3   0   0 |  0   3  0   0  1  0   0   0   0 |  * 40  *  *   *   *  *  *  *   *   *   * | 0  1  0  0  3  0   0 0  0  0 | 0  3  0  0  3 0 | 0  4
ox.. .... xo.. .... .... ....&#x  & ♦  2  2 |  1   4  1   0   0 |  0   2  2   0  0  0   0   0   0 |  *  * 60  *   *   *  *  *  *   *   *   * | 0  1  0  0  0  3   0 0  0  0 | 0  3  3  0  0 0 | 1  3
.... .... xo..3ox.. .... ....&#x  & ♦  3  3 |  3   6  0   3   0 |  1   0  3   3  0  1   0   0   0 |  *  *  * 60   *   *  *  *  *   *   *   * | 0  0  2  0  0  2   0 0  0  0 | 1  1  4  0  0 0 | 2  2
.... .... .... ox..3oo.. ....&#x  & ♦  1  3 |  0   3  0   3   0 |  0   0  0   3  0  0   1   0   0 |  *  *  *  * 120   *  *  *  *   *   *   * | 0  0  1  1  0  0   2 0  0  0 | 1  0  2  2  1 0 | 1  3
oxo. .... .... oxo. .... ....&#xt & ♦  1  5 |  0   4  2   2   4 |  0   2  0   2  0  0   0   2   2 |  *  *  *  *   * 180  *  *  *   *   *   * | 0  0  0  0  1  1   2 0  0  0 | 0  1  2  1  2 0 | 1  3
.... .... .o..3.x..3.o.. ....     & ♦  0  6 |  0   0  0  12   0 |  0   0  0   0  0  4   4   0   0 |  *  *  *  *   *   * 30  *  *   *   *   * | 0  0  1  0  0  0   0 1  0  2 | 1  0  2  1  0 2 | 3  1
.... .... .... .x..3.o..3.o..     & ♦  0  4 |  0   0  0   6   0 |  0   0  0   0  0  0   4   0   0 |  *  *  *  *   *   *  * 30  *   *   *   * | 0  0  0  1  0  0   0 1  0  2 | 1  0  1  2  0 2 | 3  1
.xo.3.ox. .... .... .... ....&#x    ♦  0  6 |  0   0  6   0   6 |  0   0  0   0  2  0   0   6   0 |  *  *  *  *   *   *  *  * 30   *   *   * | 0  0  0  0  4  0   0 0  0  0 | 0  2  0  0  4 0 | 0  4
.xo. .... .... .... .ox. ....&#x  & ♦  0  4 |  0   0  1   1   4 |  0   0  0   0  0  0   0   2   2 |  *  *  *  *   *   *  *  *  * 180   *   * | 0  0  0  0  1  0   2 0  1  0 | 0  1  1  2  2 0 | 1  3
.... .... .oo.3.xo. .... ....&#x  & ♦  0  4 |  0   0  0   3   3 |  0   0  0   0  0  1   0   0   3 |  *  *  *  *   *   *  *  *  *   * 120   * | 0  0  0  0  0  1   0 0  1  2 | 0  1  2  2  0 1 | 2  2
.... .... .... .xo.3.ox. ....&#x    ♦  0  6 |  0   0  0   6   6 |  0   0  0   0  0  0   2   0   6 |  *  *  *  *   *   *  *  *  *   *   * 120 | 0  0  0  0  0  0   2 0  0  2 | 0  0  2  2  1 1 | 2  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 | 2  *  *  *  *  *   * *  *  * | 3  0  0  0  0 0 | 3  0
ox..3oo.. xo.. .... .... ....&#x  & ♦  2  3 |  1   6  3   0   0 |  0   6  3   0  1  0   0   0   0 |  0  2  3  0   0   0  0  0  0   0   0   0 | * 20  *  *  *  *   * *  *  * | 0  3  0  0  0 0 | 0  3
.... .... xo..3ox..3oo.. ....&#x  & ♦  4  6 |  6  12  0  12   0 |  4   0  6  12  0  4   4   0   0 |  1  0  0  4   4   0  1  0  0   0   0   0 | *  * 30  *  *  *   * *  *  * | 1  0  2  0  0 0 | 2  1
.... .... .... ox..3oo..3oo..&#x  & ♦  1  4 |  0   4  0   6   0 |  0   0  0   6  0  0   4   0   0 |  0  0  0  0   4   0  0  1  0   0   0   0 | *  *  * 30  *  *   * *  *  * | 1  0  0  2  0 0 | 2  1
oxo.3oox. .... oxo. .... ....&#xt & ♦  1  9 |  0   6  9   3  12 |  0   6  0   3  3  0   0  12   6 |  0  2  0  0   0   3  0  0  2   3   0   0 | *  *  *  * 60  *   * *  *  * | 0  1  0  0  2 0 | 0  3
oxo. .... xoo.3oxo. .... ....&#xt & ♦  3  7 |  3  12  3   6   6 |  1   6  6   6  0  2   0   3   6 |  0  0  3  2   0   3  0  0  0   0   2   0 | *  *  *  *  * 60   * *  *  * | 0  1  2  0  0 0 | 1  2
oxo. .... .... oxo.3oox. ....&#xt & ♦  1  9 |  0   6  3   9  12 |  0   3  0   6  0  0   3   6  12 |  0  0  0  0   2   3  0  0  0   3   0   2 | *  *  *  *  *  * 120 *  *  * | 0  0  1  1  1 0 | 1  2
.... .... .o..3.x..3.o..3.o..     & ♦  0 10 |  0   0  0  30   0 |  0   0  0   0  0 10  20   0   0 |  0  0  0  0   0   0  5  5  0   0   0   0 | *  *  *  *  *  *   * 6  *  * | 1  0  0  0  0 2 | 3  0
.xo. .... .... .... .ox.3.oo.&#x  & ♦  0  5 |  0   0  1   3   6 |  0   0  0   0  0  1   0   3   6 |  0  0  0  0   0   0  0  0  0   3   2   0 | *  *  *  *  *  *   * * 60  * | 0  1  0  2  0 0 | 1  2
.... .... .oo.3.xo.3.ox. ....&#x  & ♦  0 10 |  0   0  0  18  12 |  0   0  0   0  0  4   8   0  18 |  0  0  0  0   0   0  1  1  0   0   4   4 | *  *  *  *  *  *   * *  * 60 | 0  0  1  1  0 1 | 2  1
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... xo..3ox..3oo..3oo..&#x  & ♦  5 10 | 10  20  0  30   0 | 10   0 10  30  0 10  20   0   0 |  5  0  0 10  20   0  5  5  0   0   0   0 | 1  0  5  5  0  0   0 1  0  0 | 6  *  *  *  * * | 2  0
oxo.3oox. xoo.3oxo. .... ....&#xt & ♦  3 12 |  3  18 12   9  18 |  1  18  9   9  4  3   0  18  18 |  0  6  9  3   0   9  0  0  3   9   6   0 | 0  3  0  0  3  3   0 0  3  0 | * 20  *  *  * * | 0  2
oxo. .... xoo.3oxo.3oox. ....&#xt & ♦  4 16 |  6  24  6  30  24 |  4  12 12  24  0  8  12  12  36 |  1  0  6  8   8  12  2  1  0   6   8   8 | 0  0  2  0  0  4   4 0  0  2 | *  * 30  *  * * | 1  1
oxo. .... .... oxo.3oox.3ooo.&#xt & ♦  1 14 |  0   8  4  24  24 |  0   4  0  12  0  4  12  12  36 |  0  0  0  0   8   6  1  2  0  12   8   8 | 0  0  0  2  0  0   4 0  4  2 | *  *  * 30  * * | 1  1
oxoo3ooxo .... oxoo3ooxo ....&#xt   ♦  2 18 |  0  18 18  18  36 |  0  18  0  18  6  0   6  36  36 |  0  6  0  0   6  18  0  0  6  18   0   6 | 0  0  0  0  6  0   6 0  0  0 | *  *  *  * 20 * | 0  2
.... .... .oo.3.xo.3.ox.3.oo.&#x    ♦  0 20 |  0   0  0  60  30 |  0   0  0   0  0 20  40   0  60 |  0  0  0  0   0   0 10 10  0   0  20  20 | 0  0  0  0  0  0   0 2  0 10 | *  *  *  *  * 6 | 2  0
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
oxo. .... xoo.3oxo.3oox.3ooo.&#xt & ♦  5 30 | 10  40 10  90  60 | 10  20 20  60  0 30  60  30 120 |  5  0 10 20  40  30 15 15  0  30  40  40 | 1  0 10 10  0 10  20 3 10 20 | 2  0  5  5  0 2 | 6  *
oxoo3ooxo xooo3oxoo3ooxo ....&#xt & ♦  5 30 |  6  48 30  54  72 |  4  48 18  54 10 12  24  72 108 |  1 16 18 12  24  54  3  3 12  54  24  24 | 0  6  3  3 18 12  24 0 12  6 | 0  4  3  3  4 0 | * 10


oxooo3ooxoo3oooxo oxooo3ooxoo3oooxo&#xt   → all heights = 1/2
(pt || tetdip || octdip || bidual tetdip || pt)

o....3o....3o.... o....3o....3o....     & | 2  *  * ♦ 16  0   0   0 | 48  0   0   0  0 | 32 36  0   0   0   0   0  0 |  8 48  0  0   0 | 12 16  0  0 |  8
.o...3.o...3.o... .o...3.o...3.o...     & | * 32  * ♦  1  6   9   0 |  6  6  18  18  0 |  6  9  8  18  18   6   9  0 |  2 18  6  6  24 |  6 10  6  6 |  8
..o..3..o..3..o.. ..o..3..o..3..o..       | *  * 36 ♦  0  0   8   8 |  0  0   8  32  8 |  0  2  0  16  16  16  16  2 |  0  8  8  8  32 |  4  8  8  8 |  8
------------------------------------------+---------+---------------+------------------+-----------------------------+-----------------+-------------+---
oo...3oo...3oo... oo...3oo...3oo...&#x  & | 1  1  0 | 32  *   *   * |  6  0   0   0  0 |  6  9  0   0   0   0   0  0 |  2 18  0  0   0 |  6  9  0  0 |  6
.x... ..... ..... ..... ..... .....     & | 0  2  0 |  * 96   *   * |  1  2   3   0  0 |  2  3  1   6   3   0   0  0 |  1  9  3  1   6 |  4  6  3  2 |  6
.oo..3.oo..3.oo.. .oo..3.oo..3.oo..&#x  & | 0  1  1 |  *  * 288   * |  0  0   2   4  0 |  0  1  0   4   4   2   4  0 |  0  4  2  2  12 |  2  5  4  4 |  6
..... ..x.. ..... ..... ..... .....     & | 0  0  2 |  *  *   * 144 |  0  0   0   4  2 |  0  0  0   4   2   4   4  1 |  0  2  4  2  12 |  2  4  5  4 |  6
------------------------------------------+---------+---------------+------------------+-----------------------------+-----------------+-------------+---
ox... ..... ..... ..... ..... .....&#x  & | 1  2  0 |  2  1   0   0 | 96  *   *   *  * |  2  3  0   0   0   0   0  0 |  1  9  0  0   0 |  4  6  0  0 |  5
.x...3.o... ..... ..... ..... .....     & | 0  3  0 |  0  3   0   0 |  * 64   *   *  * |  1  0  1   3   0   0   0  0 |  1  3  3  0   3 |  3  3  3  1 |  5
.xo.. ..... ..... ..... ..... .....&#x  & | 0  2  1 |  0  1   2   0 |  *  * 288   *  * |  0  1  0   2   2   0   0  0 |  0  4  1  1   4 |  2  4  2  2 |  5
..... .ox.. ..... ..... ..... .....&#x  & | 0  1  2 |  0  0   2   1 |  *  *   * 576  * |  0  0  0   1   1   1   2  0 |  0  1  1  1   7 |  1  3  3  3 |  5
..o..3..x.. ..... ..... ..... .....     & | 0  0  3 |  0  0   0   3 |  *  *   *   * 96 |  0  0  0   2   0   2   0  1 |  0  1  4  1   4 |  2  2  4  2 |  5
------------------------------------------+---------+---------------+------------------+-----------------------------+-----------------+-------------+---
ox...3oo... ..... ..... ..... .....&#x  & ♦ 1  3  0 |  3  3   0   0 |  3  1   0   0  0 | 64  *  *   *   *   *   *  * |  1  3  0  0   0 |  3  3  0  0 |  4
oxo.. ..... ..... oxo.. ..... .....&#xt & ♦ 1  4  1 |  4  4   4   0 |  4  0   4   0  0 |  * 72  *   *   *   *   *  * |  0  4  0  0   0 |  2  4  0  0 |  4
.x...3.o...3.o... ..... ..... .....     & ♦ 0  4  0 |  0  6   0   0 |  0  4   0   0  0 |  *  * 16   *   *   *   *  * |  1  0  3  0   0 |  3  0  3  0 |  4
.xo..3.ox.. ..... ..... ..... .....&#x  & ♦ 0  3  3 |  0  3   6   3 |  0  1   3   3  1 |  *  *  * 192   *   *   *  * |  0  1  1  0   2 |  1  2  1  2 |  4
.xo.. ..... ..... ..... .ox.. .....&#x  & ♦ 0  2  2 |  0  1   4   1 |  0  0   2   2  0 |  *  *  *   * 288   *   *  * |  0  1  0  1   2 |  1  2  1  2 |  4
..... .ox..3.oo.. ..... ..... .....&#x  & ♦ 0  1  3 |  0  0   3   3 |  0  0   0   3  1 |  *  *  *   *   * 192   *  * |  0  0  1  1   2 |  1  1  2  2 |  4
..... .oxo. ..... ..... .oxo. .....&#x    ♦ 0  2  4 |  0  0   8   4 |  0  0   0   8  0 |  *  *  *   *   *   * 144  * |  0  0  0  0   4 |  0  2  2  2 |  4
..o..3..x..3..o.. ..... ..... .....     & ♦ 0  0  6 |  0  0   0  12 |  0  0   0   0  8 |  *  *  *   *   *   *   * 12 |  0  0  4  0   0 |  2  0  4  0 |  4
------------------------------------------+---------+---------------+------------------+-----------------------------+-----------------+-------------+---
ox...3oo...3oo... ..... ..... .....&#x  & ♦ 1  4  0 |  4  6   0   0 |  6  4   0   0  0 |  4  0  1   0   0   0   0  0 | 16  *  *  *   * |  3  0  0  0 |  3
oxo..3oox.. ..... oxo.. ..... .....&#xt & ♦ 1  6  3 |  6  9  12   3 |  9  2  12   6  1 |  2  3  0   2   3   0   0  0 |  * 96  *  *   * |  1  2  0  0 |  3
.xo..3.ox..3.oo.. ..... ..... .....&#x  & ♦ 0  4  6 |  0  6  12  12 |  0  4   6  12  8 |  0  0  1   4   0   4   0  1 |  *  * 48  *   * |  1  0  2  0 |  3
..... .ox..3.oo.. .xo.. ..... .....&#x  & ♦ 0  2  3 |  0  1   6   3 |  0  0   3   6  1 |  0  0  0   0   3   2   0  0 |  *  *  * 96   * |  1  0  0  2 |  3
..... .oxo.3.oox. ..... .oxo. .....&#xt & ♦ 0  4  6 |  0  3  18   9 |  0  1   6  21  2 |  0  0  0   2   3   2   3  0 |  *  *  *  * 192 |  0  1  1  1 |  3
------------------------------------------+---------+---------------+------------------+-----------------------------+-----------------+-------------+---
oxo..3oox..3ooo.. oxo.. ..... .....&#xt & ♦ 1  8  6 |  8 16  24  12 | 16  8  24  24  8 |  8  6  2   8  12   8   0  1 |  2  4  2  4   0 | 24  *  *  * |  2
oxoo.3ooxo. ..... oxoo.3ooxo. .....&#xt & ♦ 1 10  9 |  9 18  45  18 | 18  6  36  54  6 |  6  9  0  12  18   6   9  0 |  0  6  0  0   6 |  * 32  *  * |  2
.xoo.3.oxo.3.oox. ..... .oxo. .....&#xt & ♦ 0  8 12 |  0 12  48  30 |  0  8  24  72 16 |  0  0  2  16  12  16  12  2 |  0  0  4  0   8 |  *  * 24  * |  2
.xoo.3.oxo. ..... ..... .oxo.3.oox.&#xt & ♦ 0  6  9 |  0  6  36  18 |  0  2  18  54  6 |  0  0  0   6  18  12   9  0 |  0  0  0  6   6 |  *  *  * 32 |  2
------------------------------------------+---------+---------------+------------------+-----------------------------+-----------------+-------------+---
oxoo.3ooxo.3ooox. oxoo.3ooxo. .....&#xt & ♦ 1 16 18 | 12 36 108  54 | 30 20  90 180 30 | 16 18  4  48  72  48  36  3 |  3 18  9 18  36 |  3  4  3  4 | 16

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