Acronym | tracube |
Name | triangle - cube duoprism |
|,>,O device | line pyramid prism prism prism = |>||| |
Circumradius | sqrt(13/12) = 1.040833 |
Volume | sqrt(3)/4 = 0.433013 |
Face vector | 24, 60, 62, 33, 9 |
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x3o o3o4x . . . . . | 24 | 2 3 | 1 6 3 | 3 6 1 | 3 2 ----------+----+-------+---------+---------+---- x . . . . | 2 | 24 * | 1 3 0 | 3 3 0 | 3 1 . . . . x | 2 | * 36 | 0 2 2 | 1 4 1 | 2 2 ----------+----+-------+---------+---------+---- x3o . . . | 3 | 3 0 | 8 * * | 3 0 0 | 3 0 x . . . x | 4 | 2 2 | * 36 * | 1 2 0 | 2 1 . . . o4x | 4 | 0 4 | * * 18 | 0 2 1 | 1 2 ----------+----+-------+---------+---------+---- x3o . . x ♦ 6 | 6 3 | 2 3 0 | 12 * * | 2 0 x . . o4x ♦ 8 | 4 8 | 0 4 2 | * 18 * | 1 1 . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * 3 | 0 2 ----------+----+-------+---------+---------+---- x3o . o4x ♦ 12 | 12 12 | 4 12 3 | 4 3 0 | 6 * x . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 6 2 | * 3 snubbed forms: x3o2o3o4s
x x3o x4o . . . . . | 24 | 1 2 2 | 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1 ----------+----+----------+--------------+------------+------ x . . . . | 2 | 12 * * | 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0 . x . . . | 2 | * 24 * | 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1 . . . x . | 2 | * * 24 | 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1 ----------+----+----------+--------------+------------+------ x x . . . | 4 | 2 2 0 | 12 * * * * | 1 2 0 0 0 | 2 1 0 x . . x . | 4 | 2 0 2 | * 12 * * * | 0 2 1 0 0 | 1 2 0 . x3o . . | 3 | 0 3 0 | * * 8 * * | 1 0 0 2 0 | 2 0 1 . x . x . | 4 | 0 2 2 | * * * 24 * | 0 1 0 1 1 | 1 1 1 . . . x4o | 4 | 0 0 4 | * * * * 6 | 0 0 1 0 2 | 0 2 1 ----------+----+----------+--------------+------------+------ x x3o . . ♦ 6 | 3 6 0 | 3 0 2 0 0 | 4 * * * * | 2 0 0 x x . x . ♦ 8 | 4 4 4 | 2 2 0 2 0 | * 12 * * * | 1 1 0 x . . x4o ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 3 * * | 0 2 0 . x3o x . ♦ 6 | 0 6 3 | 0 0 2 3 0 | * * * 8 * | 1 0 1 . x . x4o ♦ 8 | 0 4 8 | 0 0 0 4 2 | * * * * 6 | 0 1 1 ----------+----+----------+--------------+------------+------ x x3o x . ♦ 12 | 6 12 6 | 6 3 4 6 0 | 2 3 0 2 0 | 4 * * x x . x4o ♦ 16 | 8 8 16 | 4 8 0 8 4 | 0 4 2 0 2 | * 3 * . x3o x4o ♦ 12 | 0 12 12 | 0 0 4 12 3 | 0 0 0 4 3 | * * 2
x x x x3o . . . . . | 24 | 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ----------+----+-------------+------------------+---------------+-------- x . . . . | 2 | 12 * * * | 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x . . . | 2 | * 12 * * | 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x . . | 2 | * * 12 * | 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x . | 2 | * * * 24 | 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ----------+----+-------------+------------------+---------------+-------- x x . . . | 4 | 2 2 0 0 | 6 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 6 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 12 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x x . . | 4 | 0 2 2 0 | * * * 6 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 12 * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x x . | 4 | 0 0 2 2 | * * * * * 12 * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . x3o | 3 | 0 0 0 3 | * * * * * * 8 | 0 0 0 1 0 1 1 | 0 1 1 1 ----------+----+-------------+------------------+---------------+-------- x x x . . ♦ 8 | 4 4 4 0 | 2 2 0 2 0 0 0 | 3 * * * * * * | 2 0 0 0 x x . x . ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 0 | * 6 * * * * * | 1 1 0 0 x . x x . ♦ 8 | 4 0 4 4 | 0 2 2 0 0 2 0 | * * 6 * * * * | 1 0 1 0 x . . x3o ♦ 6 | 3 0 0 6 | 0 0 3 0 0 0 2 | * * * 4 * * * | 0 1 1 0 . x x x . ♦ 8 | 0 4 4 4 | 0 0 0 2 2 2 0 | * * * * 6 * * | 1 0 0 1 . x . x3o ♦ 6 | 0 3 0 6 | 0 0 0 0 3 0 2 | * * * * * 4 * | 0 1 0 1 . . x x3o ♦ 6 | 0 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * 4 | 0 0 1 1 ----------+----+-------------+------------------+---------------+-------- x x x x . ♦ 16 | 8 8 8 8 | 4 4 4 4 4 4 0 | 2 2 2 0 2 0 0 | 3 * * * x x . x3o ♦ 12 | 6 6 0 12 | 3 0 6 0 6 0 4 | 0 3 0 2 0 2 0 | * 2 * * x . x x3o ♦ 12 | 6 0 6 12 | 0 3 6 0 0 6 4 | 0 0 3 2 0 0 2 | * * 2 * . x x x3o ♦ 12 | 0 6 6 12 | 0 0 0 3 6 6 4 | 0 0 0 0 3 2 2 | * * * 2
xx3oo xx4oo&#x → height = 1
(tisdip || tisdip)
o.3o. o.4o. | 12 * | 2 2 1 0 0 | 1 4 1 2 2 0 0 0 | 2 2 1 4 1 0 0 | 1 2 2 0
.o3.o .o4.o | * 12 | 0 0 1 2 2 | 0 0 0 2 2 1 4 1 | 0 0 1 4 1 2 2 | 0 2 2 1
---------------+-------+----------------+---------------------+----------------+--------
x. .. .. .. | 2 0 | 12 * * * * | 1 2 0 1 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0
.. .. x. .. | 2 0 | * 12 * * * | 0 2 1 0 1 0 0 0 | 1 2 0 2 1 0 0 | 1 1 2 0
oo3oo oo4oo&#x | 1 1 | * * 12 * * | 0 0 0 2 2 0 0 0 | 0 0 1 4 1 0 0 | 0 2 2 0
.x .. .. .. | 0 2 | * * * 12 * | 0 0 0 1 0 1 2 0 | 0 0 1 2 0 2 1 | 0 2 1 1
.. .. .x .. | 0 2 | * * * * 12 | 0 0 0 0 1 0 2 1 | 0 0 0 2 1 1 2 | 0 1 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | 4 * * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 12 * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
.. .. x.4o. | 4 0 | 0 4 0 0 0 | * * 3 * * * * * | 0 2 0 0 1 0 0 | 1 0 2 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 12 * * * * | 0 0 1 2 0 0 0 | 0 2 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * 12 * * * | 0 0 0 2 1 0 0 | 0 1 2 0
.x3.o .. .. | 0 3 | 0 0 0 3 0 | * * * * * 4 * * | 0 0 1 0 0 2 0 | 0 2 0 1
.x .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * * 12 * | 0 0 0 1 0 1 1 | 0 1 1 1
.. .. .x4.o | 0 4 | 0 0 0 0 4 | * * * * * * * 3 | 0 0 0 0 1 0 2 | 0 0 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 | 4 * * * * * * | 1 1 0 0
x. .. x.4o. ♦ 8 0 | 4 8 0 0 0 | 0 4 2 0 0 0 0 0 | * 3 * * * * * | 1 0 1 0
xx3oo .. ..&#x ♦ 3 3 | 3 0 3 3 0 | 1 0 0 3 0 1 0 0 | * * 4 * * * * | 0 2 0 0
xx .. xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 0 1 0 2 2 0 1 0 | * * * 12 * * * | 0 1 1 0
.. .. xx4oo&#x ♦ 4 4 | 0 4 4 0 4 | 0 0 1 0 4 0 0 1 | * * * * 3 * * | 0 0 2 0
.x3.o .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 2 3 0 | * * * * * 4 * | 0 1 0 1
.x .. .x4.o ♦ 0 8 | 0 0 0 4 8 | 0 0 0 0 0 0 4 2 | * * * * * * 3 | 0 0 1 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x.4o. ♦ 12 0 | 12 12 0 0 0 | 4 12 3 0 0 0 0 0 | 4 3 0 0 0 0 0 | 1 * * *
xx3oo xx ..&#x ♦ 6 6 | 6 3 6 6 3 | 2 3 0 6 3 2 3 0 | 1 0 2 3 0 1 0 | * 4 * *
xx .. xx4oo&#x ♦ 8 8 | 4 8 8 4 8 | 0 4 2 4 8 0 4 2 | 0 1 0 4 2 0 1 | * * 3 *
.x3.o .x4.o ♦ 0 12 | 0 0 0 12 12 | 0 0 0 0 0 4 12 3 | 0 0 0 0 0 4 3 | * * * 1
xx3oo xx xx&#x → height = 1
(tisdip || tisdip)
o.3o. o. o. | 12 * | 2 1 1 1 0 0 0 | 1 2 2 1 2 1 1 0 0 0 0 | 1 1 2 1 2 2 1 0 0 0 | 1 1 1 2 0
.o3.o .o .o | * 12 | 0 0 0 1 2 1 1 | 0 0 0 0 2 1 1 1 2 2 1 | 0 0 0 1 2 2 1 1 1 2 | 0 1 1 2 1
---------------+-------+------------------+------------------------+---------------------+----------
x. .. .. .. | 2 0 | 12 * * * * * * | 1 1 1 0 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.. .. x. .. | 2 0 | * 6 * * * * * | 0 2 0 1 0 1 0 0 0 0 0 | 1 0 2 0 2 0 1 0 0 0 | 1 1 0 2 0
.. .. .. x. | 2 0 | * * 6 * * * * | 0 0 2 1 0 0 1 0 0 0 0 | 0 1 2 0 0 2 1 0 0 0 | 1 0 1 2 0
oo3oo oo oo&#x | 1 1 | * * * 12 * * * | 0 0 0 0 2 1 1 0 0 0 0 | 0 0 0 1 2 2 1 0 0 0 | 0 1 1 2 0
.x .. .. .. | 0 2 | * * * * 12 * * | 0 0 0 0 1 0 0 1 1 1 0 | 0 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1
.. .. .x .. | 0 2 | * * * * * 6 * | 0 0 0 0 0 1 0 0 2 0 1 | 0 0 0 0 2 0 1 1 0 2 | 0 1 0 2 1
.. .. .. .x | 0 2 | * * * * * * 6 | 0 0 0 0 0 0 1 0 0 2 1 | 0 0 0 0 0 2 1 0 1 2 | 0 0 1 2 1
---------------+-------+------------------+------------------------+---------------------+----------
x.3o. .. .. | 3 0 | 3 0 0 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 0 0 | * 6 * * * * * * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
x. .. .. x. | 4 0 | 2 0 2 0 0 0 0 | * * 6 * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
.. .. x. x. | 4 0 | 0 2 2 0 0 0 0 | * * * 3 * * * * * * * | 0 0 2 0 0 0 1 0 0 0 | 1 0 0 2 0
xx .. .. ..&#x | 2 2 | 1 0 0 2 1 0 0 | * * * * 12 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.. .. xx ..&#x | 2 2 | 0 1 0 2 0 1 0 | * * * * * 6 * * * * * | 0 0 0 0 2 0 1 0 0 0 | 0 1 0 2 0
.. .. .. xx&#x | 2 2 | 0 0 1 2 0 0 1 | * * * * * * 6 * * * * | 0 0 0 0 0 2 1 0 0 0 | 0 0 1 2 0
.x3.o .. .. | 0 3 | 0 0 0 0 3 0 0 | * * * * * * * 4 * * * | 0 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1
.x .. .x .. | 0 4 | 0 0 0 0 2 2 0 | * * * * * * * * 6 * * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
.x .. .. .x | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * * * 6 * | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
.. .. .x .x | 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * * * 3 | 0 0 0 0 0 0 1 0 0 2 | 0 0 0 2 1
---------------+-------+------------------+------------------------+---------------------+----------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 0 0 | 2 3 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * | 1 1 0 0 0
x.3o. .. x. ♦ 6 0 | 6 0 3 0 0 0 0 | 2 0 3 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * | 1 0 1 0 0
x. .. x. x. ♦ 8 0 | 4 4 4 0 0 0 0 | 0 2 2 2 0 0 0 0 0 0 0 | * * 3 * * * * * * * | 1 0 0 1 0
xx3oo .. ..&#x ♦ 3 3 | 3 0 0 3 3 0 0 | 1 0 0 0 3 0 0 1 0 0 0 | * * * 4 * * * * * * | 0 1 1 0 0
xx .. xx ..&#x ♦ 4 4 | 2 2 0 4 2 2 0 | 0 1 0 0 2 2 0 0 1 0 0 | * * * * 6 * * * * * | 0 1 0 1 0
xx .. .. xx&#x ♦ 4 4 | 2 0 2 4 2 0 2 | 0 0 1 0 2 0 2 0 0 1 0 | * * * * * 6 * * * * | 0 0 1 1 0
.. .. xx xx&#x ♦ 4 4 | 0 2 2 4 0 2 2 | 0 0 0 1 0 2 2 0 0 0 1 | * * * * * * 3 * * * | 0 0 0 2 0
.x3.o .x .. ♦ 0 6 | 0 0 0 0 6 3 0 | 0 0 0 0 0 0 0 2 3 0 0 | * * * * * * * 2 * * | 0 1 0 0 1
.x3.o .. .x ♦ 0 6 | 0 0 0 0 6 0 3 | 0 0 0 0 0 0 0 2 0 3 0 | * * * * * * * * 2 * | 0 0 1 0 1
.x .. .x .x ♦ 0 8 | 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * 3 | 0 0 0 1 1
---------------+-------+------------------+------------------------+---------------------+----------
x.3o. x. x. ♦ 12 0 | 12 6 6 0 0 0 0 | 4 6 6 3 0 0 0 0 0 0 0 | 2 2 3 0 0 0 0 0 0 0 | 1 * * * *
xx3oo xx ..&#x ♦ 6 6 | 6 3 0 6 6 3 0 | 2 3 0 0 6 3 0 2 3 0 0 | 1 0 0 2 3 0 0 1 0 0 | * 2 * * *
xx3oo .. xx&#x ♦ 6 6 | 6 0 3 6 6 0 3 | 2 0 3 0 6 0 3 2 0 3 0 | 0 1 0 2 0 3 0 0 1 0 | * * 2 * *
xx .. xx xx&#x ♦ 8 8 | 4 4 4 8 4 4 4 | 0 2 2 2 4 4 4 0 2 2 2 | 0 0 1 0 2 2 2 0 0 1 | * * * 3 *
.x3.o .x .x ♦ 0 12 | 0 0 0 0 12 6 6 | 0 0 0 0 0 0 0 4 6 6 3 | 0 0 0 0 0 0 0 2 2 3 | * * * * 1
ox xx xx4oo&#x → height = sqrt(3)/2 = 0.866025
(cube || tes)
o. o. o.4o. | 8 * | 1 2 2 0 0 0 | 2 1 1 2 4 0 0 0 0 | 1 1 2 4 2 0 0 0 | 2 1 2 0
.o .o .o4.o | * 16 | 0 0 1 1 1 2 | 0 0 1 1 2 1 2 2 1 | 0 1 2 2 1 2 1 1 | 2 1 1 1
---------------+------+---------------+--------------------+-----------------+--------
.. x. .. .. | 2 0 | 4 * * * * * | 2 0 0 2 0 0 0 0 0 | 1 1 0 4 0 0 0 0 | 2 0 2 0
.. .. x. .. | 2 0 | * 8 * * * * | 1 1 0 0 2 0 0 0 0 | 1 0 1 2 2 0 0 0 | 1 1 2 0
oo oo oo4oo&#x | 1 1 | * * 16 * * * | 0 0 1 1 2 0 0 0 0 | 0 1 2 2 1 0 0 0 | 2 1 1 0
.x .. .. .. | 0 2 | * * * 8 * * | 0 0 1 0 0 1 2 0 0 | 0 1 2 0 0 2 1 0 | 2 1 0 1
.. .x .. .. | 0 2 | * * * * 8 * | 0 0 0 1 0 1 0 2 0 | 0 1 0 2 0 2 0 1 | 2 0 1 1
.. .. .x .. | 0 2 | * * * * * 16 | 0 0 0 0 1 0 1 1 1 | 0 0 1 1 1 1 1 1 | 1 1 1 1
---------------+------+---------------+--------------------+-----------------+--------
.. x. x. .. | 4 0 | 2 2 0 0 0 0 | 4 * * * * * * * * | 1 0 0 2 0 0 0 0 | 1 0 2 0
.. .. x.4o. | 4 0 | 0 4 0 0 0 0 | * 2 * * * * * * * | 1 0 0 0 2 0 0 0 | 0 1 2 0
ox .. .. ..&#x | 1 2 | 0 0 2 1 0 0 | * * 8 * * * * * * | 0 1 2 0 0 0 0 0 | 2 1 0 0
.. xx .. ..&#x | 2 2 | 1 0 2 0 1 0 | * * * 8 * * * * * | 0 1 0 2 0 0 0 0 | 2 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 0 1 | * * * * 16 * * * * | 0 0 1 1 1 0 0 0 | 1 1 1 0
.x .x .. .. | 0 4 | 0 0 0 2 2 0 | * * * * * 4 * * * | 0 1 0 0 0 2 0 0 | 2 0 0 1
.x .. .x .. | 0 4 | 0 0 0 2 0 2 | * * * * * * 8 * * | 0 0 1 0 0 1 1 0 | 1 1 0 1
.. .x .x .. | 0 4 | 0 0 0 0 2 2 | * * * * * * * 8 * | 0 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x4.o | 0 4 | 0 0 0 0 0 4 | * * * * * * * * 4 | 0 0 0 0 1 0 1 1 | 0 1 1 1
---------------+------+---------------+--------------------+-----------------+--------
.. x. x.4o. ♦ 8 0 | 4 8 0 0 0 0 | 4 2 0 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
ox xx .. ..&#x ♦ 2 4 | 1 0 4 2 2 0 | 0 0 2 2 0 1 0 0 0 | * 4 * * * * * * | 2 0 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1 4 2 0 2 | 0 0 2 0 2 0 1 0 0 | * * 8 * * * * * | 1 1 0 0
.. xx xx ..&#x ♦ 4 4 | 2 2 4 0 2 2 | 1 0 0 2 2 0 0 1 0 | * * * 8 * * * * | 1 0 1 0
.. .. xx4oo&#x ♦ 4 4 | 0 4 4 0 0 4 | 0 1 0 0 4 0 0 0 1 | * * * * 4 * * * | 0 1 1 0
.x .x .x .. ♦ 0 8 | 0 0 0 4 4 4 | 0 0 0 0 0 2 2 2 0 | * * * * * 4 * * | 1 0 0 1
.x .. .x4.o ♦ 0 8 | 0 0 0 4 0 8 | 0 0 0 0 0 0 4 0 2 | * * * * * * 2 * | 0 1 0 1
.. .x .x4.o ♦ 0 8 | 0 0 0 0 4 8 | 0 0 0 0 0 0 0 4 2 | * * * * * * * 2 | 0 0 1 1
---------------+------+---------------+--------------------+-----------------+--------
ox xx xx ..&#x ♦ 4 8 | 2 2 8 4 4 4 | 1 0 4 4 4 2 2 2 0 | 0 2 2 2 0 1 0 0 | 4 * * *
ox .. xx4oo&#x ♦ 4 8 | 0 4 8 4 0 8 | 0 1 4 0 8 0 4 0 2 | 0 0 4 0 2 0 1 0 | * 2 * *
.. xx xx4oo&#x ♦ 8 8 | 4 8 8 0 4 8 | 4 2 0 4 8 0 0 4 2 | 1 0 0 4 2 0 0 1 | * * 2 *
.x .x .x4.o ♦ 0 16 | 0 0 0 8 8 16 | 0 0 0 0 0 4 8 8 4 | 0 0 0 0 0 4 2 2 | * * * 1
ox xx xx xx&#x → height = sqrt(3)/2 = 0.866025
(cube || tes)
o. o. o. o. | 8 * | 1 1 1 2 0 0 0 0 | 1 1 1 1 2 2 2 0 0 0 0 0 0 | 1 1 1 1 2 2 2 0 0 0 0 | 1 1 1 2 0
.o .o .o .o | * 16 | 0 0 0 1 1 1 1 1 | 0 0 0 1 1 1 1 1 1 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
---------------+------+------------------+---------------------------+-----------------------+----------
.. x. .. .. | 2 0 | 4 * * * * * * * | 1 1 0 0 2 0 0 0 0 0 0 0 0 | 1 1 0 0 2 2 0 0 0 0 0 | 1 1 0 2 0
.. .. x. .. | 2 0 | * 4 * * * * * * | 1 0 1 0 0 2 0 0 0 0 0 0 0 | 1 0 1 0 2 0 2 0 0 0 0 | 1 0 1 2 0
.. .. .. x. | 2 0 | * * 4 * * * * * | 0 1 1 0 0 0 2 0 0 0 0 0 0 | 1 0 0 1 0 2 2 0 0 0 0 | 0 1 1 2 0
oo oo oo oo&#x | 1 1 | * * * 16 * * * * | 0 0 0 1 1 1 1 0 0 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.x .. .. .. | 0 2 | * * * * 8 * * * | 0 0 0 1 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1
.. .x .. .. | 0 2 | * * * * * 8 * * | 0 0 0 0 1 0 0 1 0 0 1 1 0 | 0 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
.. .. .x .. | 0 2 | * * * * * * 8 * | 0 0 0 0 0 1 0 0 1 0 1 0 1 | 0 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1
.. .. .. .x | 0 2 | * * * * * * * 8 | 0 0 0 0 0 0 1 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
---------------+------+------------------+---------------------------+-----------------------+----------
.. x. x. .. | 4 0 | 2 2 0 0 0 0 0 0 | 2 * * * * * * * * * * * * | 1 0 0 0 2 0 0 0 0 0 0 | 1 0 0 2 0
.. x. .. x. | 4 0 | 2 0 2 0 0 0 0 0 | * 2 * * * * * * * * * * * | 1 0 0 0 0 2 0 0 0 0 0 | 0 1 0 2 0
.. .. x. x. | 4 0 | 0 2 2 0 0 0 0 0 | * * 2 * * * * * * * * * * | 1 0 0 0 0 0 2 0 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x | 1 2 | 0 0 0 2 1 0 0 0 | * * * 8 * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
.. xx .. ..&#x | 2 2 | 1 0 0 2 0 1 0 0 | * * * * 8 * * * * * * * * | 0 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 0 2 0 0 1 0 | * * * * * 8 * * * * * * * | 0 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0
.. .. .. xx&#x | 2 2 | 0 0 1 2 0 0 0 1 | * * * * * * 8 * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
.x .x .. .. | 0 4 | 0 0 0 0 2 2 0 0 | * * * * * * * 4 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
.x .. .x .. | 0 4 | 0 0 0 0 2 0 2 0 | * * * * * * * * 4 * * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
.x .. .. .x | 0 4 | 0 0 0 0 2 0 0 2 | * * * * * * * * * 4 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
.. .x .x .. | 0 4 | 0 0 0 0 0 2 2 0 | * * * * * * * * * * 4 * * | 0 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
.. .x .. .x | 0 4 | 0 0 0 0 0 2 0 2 | * * * * * * * * * * * 4 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
.. .. .x .x | 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+------+------------------+---------------------------+-----------------------+----------
.. x. x. x. ♦ 8 0 | 4 4 4 0 0 0 0 0 | 2 2 2 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 0 0 0 2 0
ox xx .. ..&#x ♦ 2 4 | 1 0 0 4 2 2 0 0 | 0 0 0 2 2 0 0 1 0 0 0 0 0 | * 4 * * * * * * * * * | 1 1 0 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1 0 4 2 0 2 0 | 0 0 0 2 0 2 0 0 1 0 0 0 0 | * * 4 * * * * * * * * | 1 0 1 0 0
ox .. .. xx&#x ♦ 2 4 | 0 0 1 4 2 0 0 2 | 0 0 0 2 0 0 2 0 0 1 0 0 0 | * * * 4 * * * * * * * | 0 1 1 0 0
.. xx xx ..&#x ♦ 4 4 | 2 2 0 4 0 2 2 0 | 1 0 0 0 2 2 0 0 0 0 1 0 0 | * * * * 4 * * * * * * | 1 0 0 1 0
.. xx .. xx&#x ♦ 4 4 | 2 0 2 4 0 2 0 2 | 0 1 0 0 2 0 2 0 0 0 0 1 0 | * * * * * 4 * * * * * | 0 1 0 1 0
.. .. xx xx&#x ♦ 4 4 | 0 2 2 4 0 0 2 2 | 0 0 1 0 0 2 2 0 0 0 0 0 1 | * * * * * * 4 * * * * | 0 0 1 1 0
.x .x .x .. ♦ 0 8 | 0 0 0 0 4 4 4 0 | 0 0 0 0 0 0 0 2 2 0 2 0 0 | * * * * * * * 2 * * * | 1 0 0 0 1
.x .x .. .x ♦ 0 8 | 0 0 0 0 4 4 0 4 | 0 0 0 0 0 0 0 2 0 2 0 2 0 | * * * * * * * * 2 * * | 0 1 0 0 1
.x .. .x .x ♦ 0 8 | 0 0 0 0 4 0 4 4 | 0 0 0 0 0 0 0 0 2 2 0 0 2 | * * * * * * * * * 2 * | 0 0 1 0 1
.. .x .x .x ♦ 0 8 | 0 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * * 2 | 0 0 0 1 1
---------------+------+------------------+---------------------------+-----------------------+----------
ox xx xx ..&#x ♦ 4 8 | 2 2 0 8 4 4 4 0 | 1 0 0 4 4 4 0 2 2 0 2 0 0 | 0 2 2 0 2 0 0 1 0 0 0 | 2 * * * *
ox xx .. xx&#x ♦ 4 8 | 2 0 2 8 4 4 0 4 | 0 1 0 4 4 0 4 2 0 2 0 2 0 | 0 2 0 2 0 2 0 0 1 0 0 | * 2 * * *
ox .. xx xx&#x ♦ 4 8 | 0 2 2 8 4 0 4 4 | 0 0 1 4 0 4 4 0 2 2 0 0 2 | 0 0 2 2 0 0 2 0 0 1 0 | * * 2 * *
.. xx xx xx&#x ♦ 8 8 | 4 4 4 8 0 4 4 4 | 2 2 2 0 4 4 4 0 0 0 2 2 2 | 1 0 0 0 2 2 2 0 0 0 1 | * * * 2 *
.x .x .x .x ♦ 0 16 | 0 0 0 0 8 8 8 8 | 0 0 0 0 0 0 0 4 4 4 4 4 4 | 0 0 0 0 0 0 0 2 2 2 2 | * * * * 1
xxx xxx xxx&#x → all pairwise heights = 1 o.. o.. o.. | 8 * * | 1 1 1 1 1 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 0 .o. .o. .o. | * 8 * | 0 0 0 1 0 1 1 1 1 0 0 0 | 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 | 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 | 1 0 1 1 1 1 ..o ..o ..o | * * 8 | 0 0 0 0 1 0 0 0 1 1 1 1 | 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 | 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1 ---------------+-------+-------------------------+---------------------------------------+-------------------------------+------------ x.. ... ... | 2 0 0 | 4 * * * * * * * * * * * | 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 1 0 0 ... x.. ... | 2 0 0 | * 4 * * * * * * * * * * | 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 | 1 1 1 0 1 0 ... ... x.. | 2 0 0 | * * 4 * * * * * * * * * | 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 | 1 1 0 1 1 0 oo. oo. oo.&#x | 1 1 0 | * * * 8 * * * * * * * * | 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 | 1 0 1 1 1 0 o.o o.o o.o&#x | 1 0 1 | * * * * 8 * * * * * * * | 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0 .x. ... ... | 0 2 0 | * * * * * 4 * * * * * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 | 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 | 1 0 1 1 0 1 ... .x. ... | 0 2 0 | * * * * * * 4 * * * * * | 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 | 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 | 1 0 1 0 1 1 ... ... .x. | 0 2 0 | * * * * * * * 4 * * * * | 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 | 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 | 1 0 0 1 1 1 .oo .oo .oo&#x | 0 1 1 | * * * * * * * * 8 * * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 | 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 | 0 0 1 1 1 1 ..x ... ... | 0 0 2 | * * * * * * * * * 4 * * | 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 | 0 1 1 1 0 1 ... ..x ... | 0 0 2 | * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 | 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 | 0 1 1 0 1 1 ... ... ..x | 0 0 2 | * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 | 0 1 0 1 1 1 ---------------+-------+-------------------------+---------------------------------------+-------------------------------+------------ x.. x.. ... | 4 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 x.. ... x.. | 4 0 0 | 2 0 2 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 ... x.. x.. | 4 0 0 | 0 2 2 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * * * * * | 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 | 1 1 0 0 1 0 xx. ... ...&#x | 2 2 0 | 1 0 0 2 0 1 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0 ... xx. ...&#x | 2 2 0 | 0 1 0 2 0 0 1 0 0 0 0 0 | * * * * 4 * * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0 ... ... xx.&#x | 2 2 0 | 0 0 1 2 0 0 0 1 0 0 0 0 | * * * * * 4 * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0 x.x ... ...&#x | 2 0 2 | 1 0 0 0 2 0 0 0 0 1 0 0 | * * * * * * 4 * * * * * * * * * * * * | 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0 ... x.x ...&#x | 2 0 2 | 0 1 0 0 2 0 0 0 0 0 1 0 | * * * * * * * 4 * * * * * * * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 | 0 1 1 0 1 0 ... ... x.x&#x | 2 0 2 | 0 0 1 0 2 0 0 0 0 0 0 1 | * * * * * * * * 4 * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 | 0 1 0 1 1 0 ooo ooo ooo&#x | 1 1 1 | 0 0 0 1 1 0 0 0 1 0 0 0 | * * * * * * * * * 8 * * * * * * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 1 1 1 0 .x. .x. ... | 0 4 0 | 0 0 0 0 0 2 2 0 0 0 0 0 | * * * * * * * * * * 2 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 1 .x. ... .x. | 0 4 0 | 0 0 0 0 0 2 0 2 0 0 0 0 | * * * * * * * * * * * 2 * * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 0 1 0 1 ... .x. .x. | 0 4 0 | 0 0 0 0 0 0 2 2 0 0 0 0 | * * * * * * * * * * * * 2 * * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 0 1 1 .xx ... ...&#x | 0 2 2 | 0 0 0 0 0 1 0 0 2 1 0 0 | * * * * * * * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 | 0 0 1 1 0 1 ... .xx ...&#x | 0 2 2 | 0 0 0 0 0 0 1 0 2 0 1 0 | * * * * * * * * * * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 | 0 0 1 0 1 1 ... ... .xx&#x | 0 2 2 | 0 0 0 0 0 0 0 1 2 0 0 1 | * * * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 1 ..x ..x ... | 0 0 4 | 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * * * * * 2 * * | 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 | 0 1 1 0 0 1 ..x ... ..x | 0 0 4 | 0 0 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * * * * * * * * * * 2 * | 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 | 0 1 0 1 0 1 ... ..x ..x | 0 0 4 | 0 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * * * * * 2 | 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 | 0 1 0 0 1 1 ---------------+-------+-------------------------+---------------------------------------+-------------------------------+------------ x.. x.. x.. ♦ 8 0 0 | 4 4 4 0 0 0 0 0 0 0 0 0 | 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 1 0 0 0 0 xx. xx. ...&#x ♦ 4 4 0 | 2 2 0 4 0 2 2 0 0 0 0 0 | 1 0 0 2 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * | 1 0 1 0 0 0 xx. ... xx.&#x ♦ 4 4 0 | 2 0 2 4 0 2 0 2 0 0 0 0 | 0 1 0 2 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * | 1 0 0 1 0 0 ... xx. xx.&#x ♦ 4 4 0 | 0 2 2 4 0 0 2 2 0 0 0 0 | 0 0 1 0 2 2 0 0 0 0 0 0 1 0 0 0 0 0 0 | * * * 2 * * * * * * * * * * * | 1 0 0 0 1 0 x.x x.x ...&#x ♦ 4 0 4 | 2 2 0 0 4 0 0 0 0 2 2 0 | 1 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 1 0 0 | * * * * 2 * * * * * * * * * * | 0 1 1 0 0 0 x.x ... x.x&#x ♦ 4 0 4 | 2 0 2 0 4 0 0 0 0 2 0 2 | 0 1 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 1 0 | * * * * * 2 * * * * * * * * * | 0 1 0 1 0 0 ... x.x x.x&#x ♦ 4 0 4 | 0 2 2 0 4 0 0 0 0 0 2 2 | 0 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 1 | * * * * * * 2 * * * * * * * * | 0 1 0 0 1 0 xxx ... ...&#x ♦ 2 2 2 | 1 0 0 2 2 1 0 0 2 1 0 0 | 0 0 0 1 0 0 1 0 0 2 0 0 0 1 0 0 0 0 0 | * * * * * * * 4 * * * * * * * | 0 0 1 1 0 0 ... xxx ...&#x ♦ 2 2 2 | 0 1 0 2 2 0 1 0 2 0 1 0 | 0 0 0 0 1 0 0 1 0 2 0 0 0 0 1 0 0 0 0 | * * * * * * * * 4 * * * * * * | 0 0 1 0 1 0 ... ... xxx&#x ♦ 2 2 2 | 0 0 1 2 2 0 0 1 2 0 0 1 | 0 0 0 0 0 1 0 0 1 2 0 0 0 0 0 1 0 0 0 | * * * * * * * * * 4 * * * * * | 0 0 0 1 1 0 .x. .x. .x. ♦ 0 8 0 | 0 0 0 0 0 4 4 4 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 | * * * * * * * * * * 1 * * * * | 1 0 0 0 0 1 .xx .xx ...&#x ♦ 0 4 4 | 0 0 0 0 0 2 2 0 4 2 2 0 | 0 0 0 0 0 0 0 0 0 0 1 0 0 2 2 0 1 0 0 | * * * * * * * * * * * 2 * * * | 0 0 1 0 0 1 .xx ... .xx&#x ♦ 0 4 4 | 0 0 0 0 0 2 0 2 4 2 0 2 | 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 2 0 1 0 | * * * * * * * * * * * * 2 * * | 0 0 0 1 0 1 ... .xx .xx&#x ♦ 0 4 4 | 0 0 0 0 0 0 2 2 4 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 2 0 0 1 | * * * * * * * * * * * * * 2 * | 0 0 0 0 1 1 ..x ..x ..x ♦ 0 0 8 | 0 0 0 0 0 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * * * * * * 1 | 0 1 0 0 0 1 ---------------+-------+-------------------------+---------------------------------------+-------------------------------+------------ xx. xx. xx.&#x ♦ 8 8 0 | 4 4 4 8 0 4 4 4 0 0 0 0 | 2 2 2 4 4 4 0 0 0 0 2 2 2 0 0 0 0 0 0 | 1 2 2 2 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * * x.x x.x x.x&#x ♦ 8 0 8 | 4 4 4 0 8 0 0 0 0 4 4 4 | 2 2 2 0 0 0 4 4 4 0 0 0 0 0 0 0 2 2 2 | 1 0 0 0 2 2 2 0 0 0 0 0 0 0 1 | * 1 * * * * xxx xxx ...&#x ♦ 4 4 4 | 2 2 0 4 4 2 2 0 4 2 2 0 | 1 0 0 2 2 0 2 2 0 4 1 0 0 2 2 0 1 0 0 | 0 1 0 0 1 0 0 2 2 0 0 1 0 0 0 | * * 2 * * * xxx ... xxx&#x ♦ 4 4 4 | 2 0 2 4 4 2 0 2 4 2 0 2 | 0 1 0 2 0 2 2 0 2 4 0 1 0 2 0 2 0 1 0 | 0 0 1 0 0 1 0 2 0 2 0 0 1 0 0 | * * * 2 * * ... xxx xxx&#x ♦ 4 4 4 | 0 2 2 4 4 0 2 2 4 0 2 2 | 0 0 1 0 2 2 0 2 2 4 0 0 1 0 2 2 0 0 1 | 0 0 0 1 0 0 1 0 2 2 0 0 0 1 0 | * * * * 2 * .xx .xx .xx&#x ♦ 0 8 8 | 0 0 0 0 0 4 4 4 8 4 4 4 | 0 0 0 0 0 0 0 0 0 0 2 2 2 4 4 4 2 2 2 | 0 0 0 0 0 0 0 0 0 0 1 2 2 2 1 | * * * * * 1
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