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Acronym
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bril (old: driss, alt.: rixadot)
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Name
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birectified heptapeton,
rectified hexateron atop dodecateron,
vertex figure of lin,
Gosset polytope 03,2
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Circumradius
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sqrt(6/7) = 0.925820
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Inradius
wrt. rix
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2/sqrt(21) = 0.436436
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Inradius
wrt. dot
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sqrt(3/28) = 0.327327
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Lace city
in approx. ASCII-art
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P R -- o3x3o3o3o (rix)
R r -- o3o3x3o3o (dot)
where:
P = x3o3o3o (pen)
R = o3x3o3o (rap)
r = o3o3x3o (inv. rap)
|
+-------- o3o o3o3o (point)
/ +------ x3o x3o3o (tratet)
/ / +---- o3x o3x3o (gyro troct)
/ / / +-- o3o o3o3x (dual tet)
/ / / /
p H o -- o3x3o3o3o (rix)
t O T -- o3o3x3o3o (dot)
\ \ \
| | +-- o o3o3x3o (inv. rap)
\ +----- x o3x3o3o (rappip)
+------- o x3o3o3o (pen)
where:
p = o o3o3o (point)
H = x x3o3o (tepe)
o = o o3x3o (oct)
t = o x3o3o (tet)
O = x o3x3o (ope)
T = o o3o3x (dual tet)
|
x3o o3o o3x x3o o3o o3x -- o3x3o3o3o (rix)
o3o o3o x3o x3o o3x o3x o3o o3o -- o3o3x3o3o (dot)
\ \ \ +-- (0, tet) = pen
| | +----------- (3, oct) = troct
\ +--------------------- (dual 3, dual tet) = tratet
+------------------------------ (0, 0) = point
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Volume
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151 sqrt(7)/2880 = 0.138718
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Surface
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161 sqrt(3)/120 = 2.323835
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Dihedral angles
(at margins)
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- at rap between dot and rix: arccos(-1/6) = 99.594068°
- at pen between rix and rix: arccos(1/6) = 80.405932°
- at rap between dot and dot: arccos(1/6) = 80.405932°
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Face vector
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35, 210, 350, 245, 84, 14
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Confer
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- related segmentopeta:
-
tratetpy
tratet altroct
teta troct
pena rappip
rappaf
triddippa tridafup
- related scaliforms:
-
ladbril
- ambification:
-
sabril
- general polytopal classes:
-
Wythoffian polypeta
segmentopeta
fundamental lace prisms
lace simplices
Coxeter-Elte-Gosset polytopes
- analogs:
-
birectified simplex brSn
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External
links
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When represented as oxoo3ooxo oxoo3ooxo3ooox&#xt it becomes apparent that bril allows for a heptadiminishing
by omitting the uppermost (single) vertex plus 3 mutually orthogonally chosen vertex pairs from the octs
of the third vertex layer. It further becomes apparent that those 7 vertices then mutually have a pairwise distance of
q=sqrt(2), i.e. belong to a vertex-inscribed q-scaled hop.
As a mere diminishing its according all unit-edged outcome, ladbril,
clearly is a CRF,
but it further turns out that it is scaliform as well.
Incidence matrix according to Dynkin symbol
o3o3x3o3o3o
. . . . . . | 35 ♦ 12 | 12 18 | 4 18 12 | 6 12 3 | 4 3
------------+----+-----+---------+------------+----------+----
. . x . . . | 2 | 210 | 2 3 | 1 6 3 | 3 6 1 | 3 2
------------+----+-----+---------+------------+----------+----
. o3x . . . | 3 | 3 | 140 * | 1 3 0 | 3 3 0 | 3 1
. . x3o . . | 3 | 3 | * 210 | 0 2 2 | 1 4 1 | 2 2
------------+----+-----+---------+------------+----------+----
o3o3x . . . ♦ 4 | 6 | 4 0 | 35 * * | 3 0 0 | 3 0
. o3x3o . . ♦ 6 | 12 | 4 4 | * 105 * | 1 2 0 | 2 1
. . x3o3o . ♦ 4 | 6 | 0 4 | * * 105 | 0 2 1 | 1 2
------------+----+-----+---------+------------+----------+----
o3o3x3o . . ♦ 10 | 30 | 20 10 | 5 5 0 | 21 * * | 2 0
. o3x3o3o . ♦ 10 | 30 | 10 20 | 0 5 5 | * 42 * | 1 1
. . x3o3o3o ♦ 5 | 10 | 0 10 | 0 0 5 | * * 21 | 0 2
------------+----+-----+---------+------------+----------+----
o3o3x3o3o . ♦ 20 | 90 | 60 60 | 15 30 15 | 6 6 0 | 7 *
. o3x3o3o3o ♦ 15 | 60 | 20 60 | 0 15 30 | 0 6 6 | * 7
oo3xo3ox3oo3oo&#x → height = sqrt(7/12) = 0.763763
(rix || dot)
o.3o.3o.3o.3o. | 15 * ♦ 8 4 0 | 4 12 8 6 0 0 | 6 8 4 12 4 0 0 0 | 4 2 6 8 1 0 0 | 1 4 2 0
.o3.o3.o3.o3.o | * 20 ♦ 0 3 9 | 0 0 3 9 9 9 | 0 0 1 9 9 3 9 3 | 0 0 3 9 3 3 3 | 0 3 3 1
------------------+-------+----------+-------------------+-------------------------+------------------+--------
.. x. .. .. .. | 2 0 | 60 * * | 1 3 1 0 0 0 | 3 3 1 3 0 0 0 0 | 3 1 3 3 0 0 0 | 1 3 1 0
oo3oo3oo3oo3oo&#x | 1 1 | * 60 * | 0 0 2 3 0 0 | 0 0 1 6 3 0 0 0 | 0 0 3 6 1 0 0 | 0 3 2 0
.. .. .x .. .. | 0 2 | * * 90 | 0 0 0 1 2 2 | 0 0 0 2 2 1 4 1 | 0 0 1 4 1 2 2 | 0 2 2 1
------------------+-------+----------+-------------------+-------------------------+------------------+--------
o.3x. .. .. .. | 3 0 | 3 0 0 | 20 * * * * * | 3 0 1 0 0 0 0 0 | 3 0 3 0 0 0 0 | 1 3 0 0
.. x.3o. .. .. | 3 0 | 3 0 0 | * 60 * * * * | 1 2 0 1 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0
.. xo .. .. ..&#x | 2 1 | 1 2 0 | * * 60 * * * | 0 0 1 3 0 0 0 0 | 0 0 3 3 0 0 0 | 0 3 1 0
.. .. ox .. ..&#x | 1 2 | 0 2 1 | * * * 90 * * | 0 0 0 2 2 0 0 0 | 0 0 1 4 1 0 0 | 0 2 2 0
.. .o3.x .. .. | 0 3 | 0 0 3 | * * * * 60 * | 0 0 0 1 0 1 2 0 | 0 0 1 2 0 2 1 | 0 2 1 1
.. .. .x3.o .. | 0 3 | 0 0 3 | * * * * * 60 | 0 0 0 0 1 0 2 1 | 0 0 0 2 1 1 2 | 0 1 2 1
------------------+-------+----------+-------------------+-------------------------+------------------+--------
o.3x.3o. .. .. ♦ 6 0 | 12 0 0 | 4 4 0 0 0 0 | 15 * * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0
.. x.3o.3o. .. ♦ 4 0 | 6 0 0 | 0 4 0 0 0 0 | * 30 * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
oo3xo .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 0 3 0 0 0 | * * 20 * * * * * | 0 0 3 0 0 0 0 | 0 3 0 0
.. xo3ox .. ..&#x ♦ 3 3 | 3 6 3 | 0 1 3 3 1 0 | * * * 60 * * * * | 0 0 1 2 0 0 0 | 0 2 1 0
.. .. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0 0 0 3 0 1 | * * * * 60 * * * | 0 0 0 2 1 0 0 | 0 1 2 0
.o3.o3.x .. .. ♦ 0 4 | 0 0 6 | 0 0 0 0 4 0 | * * * * * 15 * * | 0 0 1 0 0 2 0 | 0 2 0 1
.. .o3.x3.o .. ♦ 0 6 | 0 0 12 | 0 0 0 0 4 4 | * * * * * * 30 * | 0 0 0 1 0 1 1 | 0 1 1 1
.. .. .x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 0 0 0 4 | * * * * * * * 15 | 0 0 0 0 1 0 2 | 0 0 2 1
------------------+-------+----------+-------------------+-------------------------+------------------+--------
o.3x.3o.3o. .. ♦ 10 0 | 30 0 0 | 10 20 0 0 0 0 | 5 5 0 0 0 0 0 0 | 6 * * * * * * | 1 1 0 0
.. x.3o.3o.3o. ♦ 5 0 | 10 0 0 | 0 10 0 0 0 0 | 0 5 0 0 0 0 0 0 | * 6 * * * * * | 1 0 1 0
oo3xo3ox .. ..&#x ♦ 6 4 | 12 12 6 | 4 4 12 6 4 0 | 1 0 4 4 0 1 0 0 | * * 15 * * * * | 0 2 0 0
.. xo3ox3oo ..&#x ♦ 4 6 | 6 12 12 | 0 4 6 12 4 4 | 0 1 0 4 4 0 1 0 | * * * 30 * * * | 0 1 1 0
.. .. ox3oo3oo&#x ♦ 1 4 | 0 4 6 | 0 0 0 6 0 4 | 0 0 0 0 4 0 0 1 | * * * * 15 * * | 0 0 2 0
.o3.o3.x3.o .. ♦ 0 10 | 0 0 30 | 0 0 0 0 20 10 | 0 0 0 0 0 5 5 0 | * * * * * 6 * | 0 1 0 1
.. .o3.x3.o3.o ♦ 0 10 | 0 0 30 | 0 0 0 0 10 20 | 0 0 0 0 0 0 5 5 | * * * * * * 6 | 0 0 1 1
------------------+-------+----------+-------------------+-------------------------+------------------+--------
o.3x.3o.3o.3o. ♦ 15 0 | 60 0 0 | 20 60 0 0 0 0 | 15 30 0 0 0 0 0 0 | 6 6 0 0 0 0 0 | 1 * * *
oo3xo3ox3oo ..&#x ♦ 10 10 | 30 30 30 | 10 20 30 30 20 10 | 5 5 10 20 10 5 5 0 | 1 0 5 5 0 1 0 | * 6 * *
.. xo3ox3oo3oo&#x ♦ 5 10 | 10 20 30 | 0 10 10 30 10 20 | 0 5 0 10 20 0 5 5 | 0 1 0 5 5 0 1 | * * 6 *
.o3.o3.x3.o3.o ♦ 0 20 | 0 0 90 | 0 0 0 0 60 60 | 0 0 0 0 0 15 30 15 | 0 0 0 0 0 6 6 | * * * 1
oxo xoo3oxo3oox3ooo&#xt → all heights = sqrt(7/20) = 0.591608
(pen || (pseudo) rappip || inv. rap)
o.. o..3o..3o..3o.. | 5 * * ♦ 4 8 0 0 0 0 | 6 4 8 12 0 0 0 0 0 0 0 | 4 4 6 12 8 0 0 0 0 0 0 0 0 | 1 6 4 8 2 0 0 0 0 0 | 4 1 2 0
.o. .o.3.o.3.o.3.o. | * 20 * ♦ 0 2 1 6 3 0 | 0 2 1 6 3 6 3 6 3 0 0 | 0 1 6 3 6 3 2 3 3 6 1 0 0 | 0 3 6 3 2 1 1 3 2 0 | 3 2 1 1
..o ..o3..o3..o3..o | * * 10 ♦ 0 0 0 0 6 6 | 0 0 0 0 0 0 3 6 12 6 3 | 0 0 3 0 0 0 0 6 2 12 6 2 3 | 0 1 6 0 0 0 3 4 6 1 | 2 3 0 2
------------------------+---------+-------------------+----------------------------------+-------------------------------------+----------------------------+--------
... x.. ... ... ... | 2 0 0 | 10 * * * * * | 3 0 2 0 0 0 0 0 0 0 0 | 3 1 0 6 0 0 0 0 0 0 0 0 0 | 1 3 0 6 0 0 0 0 0 0 | 3 0 2 0
oo. oo.3oo.3oo.3oo.&#x | 1 1 0 | * 40 * * * * | 0 1 1 3 0 0 0 0 0 0 0 | 0 1 3 3 3 0 0 0 0 0 0 0 0 | 0 3 3 3 1 0 0 0 0 0 | 3 1 1 0
.x. ... ... ... ... | 0 2 0 | * * 10 * * * | 0 2 0 0 0 0 3 0 0 0 0 | 0 1 6 0 0 0 0 3 0 0 0 0 0 | 0 3 6 0 0 0 1 0 0 0 | 3 2 0 0
... ... .x. ... ... | 0 2 0 | * * * 60 * * | 0 0 0 1 1 2 0 1 0 0 0 | 0 0 1 1 2 2 1 0 1 2 0 0 0 | 0 1 2 2 1 1 0 2 1 0 | 2 1 1 1
.oo .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * * 60 * | 0 0 0 0 0 0 1 2 2 0 0 | 0 0 2 0 0 0 0 2 1 4 1 0 0 | 0 1 4 0 0 0 1 2 2 0 | 2 2 0 1
... ... ... ..x ... | 0 0 2 | * * * * * 30 | 0 0 0 0 0 0 0 0 2 2 1 | 0 0 0 0 0 0 0 1 0 4 2 1 2 | 0 0 2 0 0 0 1 2 4 1 | 1 2 0 2
------------------------+---------+-------------------+----------------------------------+-------------------------------------+----------------------------+--------
... x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 0 | 10 * * * * * * * * * * | 2 0 0 2 0 0 0 0 0 0 0 0 0 | 1 1 0 4 0 0 0 0 0 0 | 2 0 2 0
ox. ... ... ... ...&#x | 1 2 0 | 0 2 1 0 0 0 | * 20 * * * * * * * * * | 0 1 3 0 0 0 0 0 0 0 0 0 0 | 0 3 3 0 0 0 0 0 0 0 | 3 1 0 0
... xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * * 20 * * * * * * * * | 0 1 0 3 0 0 0 0 0 0 0 0 0 | 0 3 0 3 0 0 0 0 0 0 | 3 0 1 0
... ... ox. ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * * 60 * * * * * * * | 0 0 1 1 2 0 0 0 0 0 0 0 0 | 0 1 2 2 1 0 0 0 0 0 | 2 1 1 0
... .o.3.x. ... ... | 0 3 0 | 0 0 0 3 0 0 | * * * * 20 * * * * * * | 0 0 0 1 0 2 0 0 1 0 0 0 0 | 0 1 0 2 0 1 0 2 0 0 | 2 0 1 1
... ... .x.3.o. ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * 40 * * * * * | 0 0 0 0 1 1 1 0 0 1 0 0 0 | 0 0 1 1 1 1 0 1 1 0 | 1 1 1 1
.xo ... ... ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * * * 30 * * * * | 0 0 2 0 0 0 0 2 0 0 0 0 0 | 0 1 4 0 0 0 1 0 0 0 | 2 2 0 0
... ... .xo ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * * 60 * * * | 0 0 1 0 0 0 0 0 1 2 0 0 0 | 0 1 2 0 0 0 0 2 1 0 | 2 1 0 1
... ... ... .ox ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * * 60 * * | 0 0 0 0 0 0 0 1 0 2 1 0 0 | 0 0 2 0 0 0 1 1 2 0 | 1 2 0 1
... ... ..o3..x ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * 20 * | 0 0 0 0 0 0 0 0 0 2 0 1 1 | 0 0 1 0 0 0 0 2 2 1 | 1 1 0 2
... ... ... ..x3..o | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * 10 | 0 0 0 0 0 0 0 0 0 0 2 0 2 | 0 0 0 0 0 0 1 0 4 1 | 0 2 0 2
------------------------+---------+-------------------+----------------------------------+-------------------------------------+----------------------------+--------
... x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | 5 * * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 1 0 2 0
ox. xo. ... ... ...&#x ♦ 2 2 0 | 1 4 1 0 0 0 | 0 2 2 0 0 0 0 0 0 0 0 | * 10 * * * * * * * * * * * | 0 3 0 0 0 0 0 0 0 0 | 3 0 0 0
oxo ... oxo ... ...&#xt ♦ 1 4 1 | 0 4 2 2 4 0 | 0 2 0 2 0 0 2 2 0 0 0 | * * 30 * * * * * * * * * * | 0 1 2 0 0 0 0 0 0 0 | 2 1 0 0
... xo.3ox. ... ...&#x ♦ 3 3 0 | 3 6 0 3 0 0 | 1 0 3 3 1 0 0 0 0 0 0 | * * * 20 * * * * * * * * * | 0 1 0 2 0 0 0 0 0 0 | 2 0 1 0
... ... ox.3oo. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 0 3 0 1 0 0 0 0 0 | * * * * 40 * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 | 1 1 1 0
... .o.3.x.3.o. ... ♦ 0 6 0 | 0 0 0 12 0 0 | 0 0 0 0 4 4 0 0 0 0 0 | * * * * * 10 * * * * * * * | 0 0 0 1 0 1 0 1 0 0 | 1 0 1 1
... ... .x.3.o.3.o. ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 4 0 0 0 0 0 | * * * * * * 10 * * * * * * | 0 0 0 0 1 1 0 0 1 0 | 0 1 1 1
.xo ... ... .ox ...&#x ♦ 0 2 2 | 0 0 1 0 4 1 | 0 0 0 0 0 0 2 0 2 0 0 | * * * * * * * 30 * * * * * | 0 0 2 0 0 0 1 0 0 0 | 1 2 0 0
... .oo3.xo ... ...&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 0 1 0 0 3 0 0 0 | * * * * * * * * 20 * * * * | 0 1 0 0 0 0 0 2 0 0 | 2 0 0 1
... ... .xo3.ox ...&#x ♦ 0 3 3 | 0 0 0 3 6 3 | 0 0 0 0 0 1 0 3 3 1 0 | * * * * * * * * * 40 * * * | 0 0 1 0 0 0 0 1 1 0 | 1 1 0 1
... ... ... .ox3.oo&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 3 0 1 | * * * * * * * * * * 20 * * | 0 0 0 0 0 0 1 0 2 0 | 0 2 0 1
... ..o3..o3..x ... ♦ 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 4 0 | * * * * * * * * * * * 5 * | 0 0 0 0 0 0 0 2 0 1 | 1 0 0 2
... ... ..o3..x3..o ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * * 5 | 0 0 0 0 0 0 0 0 2 1 | 0 1 0 2
------------------------+---------+-------------------+----------------------------------+-------------------------------------+----------------------------+--------
... x..3o..3o..3o.. ♦ 5 0 0 | 10 0 0 0 0 0 | 10 0 0 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 0 0 2 0
oxo xoo3oxo ... ...&#xt ♦ 3 6 1 | 3 12 3 6 6 0 | 1 6 6 6 2 0 3 6 0 0 0 | 0 3 3 2 0 0 0 0 2 0 0 0 0 | * 10 * * * * * * * * | 2 0 0 0
oxo ... oxo3oox ...&#xt ♦ 1 6 3 | 0 6 3 6 12 3 | 0 3 0 6 0 2 6 6 6 1 0 | 0 0 3 0 2 0 0 3 0 2 0 0 0 | * * 20 * * * * * * * | 1 1 0 0
... xo.3ox.3oo. ...&#x ♦ 4 6 0 | 6 12 0 12 0 0 | 4 0 6 12 4 4 0 0 0 0 0 | 1 0 0 4 4 1 0 0 0 0 0 0 0 | * * * 10 * * * * * * | 1 0 1 0
... ... ox.3oo.3oo.&#x ♦ 1 4 0 | 0 4 0 6 0 0 | 0 0 0 6 0 4 0 0 0 0 0 | 0 0 0 0 4 0 1 0 0 0 0 0 0 | * * * * 10 * * * * * | 0 1 1 0
... .o.3.x.3.o.3.o. ♦ 0 10 0 | 0 0 0 30 0 0 | 0 0 0 0 10 20 0 0 0 0 0 | 0 0 0 0 0 5 5 0 0 0 0 0 0 | * * * * * 2 * * * * | 0 0 1 1
.xo ... ... .ox3.oo&#x ♦ 0 2 3 | 0 0 1 0 6 3 | 0 0 0 0 0 0 3 0 6 0 1 | 0 0 0 0 0 0 0 3 0 0 2 0 0 | * * * * * * 10 * * * | 0 2 0 0
... .oo3.xo3.ox ...&#x ♦ 0 6 4 | 0 0 0 12 12 6 | 0 0 0 0 4 4 0 12 6 4 0 | 0 0 0 0 0 1 0 0 4 4 0 1 0 | * * * * * * * 10 * * | 1 0 0 1
... ... .xo3.ox3.oo&#x ♦ 0 4 6 | 0 0 0 6 12 12 | 0 0 0 0 0 4 0 6 12 4 4 | 0 0 0 0 0 0 1 0 0 4 4 0 1 | * * * * * * * * 10 * | 0 1 0 1
... ..o3..o3..x3..o ♦ 0 0 10 | 0 0 0 0 0 30 | 0 0 0 0 0 0 0 0 0 20 10 | 0 0 0 0 0 0 0 0 0 0 0 5 5 | * * * * * * * * * 1 | 0 0 0 2
------------------------+---------+-------------------+----------------------------------+-------------------------------------+----------------------------+--------
oxo xoo3oxo3oox ...&#xt ♦ 4 12 4 | 6 24 6 24 24 6 | 4 12 12 24 8 8 12 24 12 4 0 | 1 6 12 8 8 2 0 6 8 8 0 1 0 | 0 4 4 2 0 0 0 2 0 0 | 5 * * *
oxo ... oxo3oox3ooo&#xt ♦ 1 8 6 | 0 8 4 12 24 12 | 0 4 0 12 0 8 12 12 24 4 4 | 0 0 6 0 8 0 2 12 0 8 8 0 1 | 0 0 4 0 2 0 4 0 2 0 | * 5 * *
... xo.3ox.3oo.3oo.&#x ♦ 5 10 0 | 10 20 0 30 0 0 | 10 0 10 30 10 20 0 0 0 0 0 | 5 0 0 10 20 5 5 0 0 0 0 0 0 | 1 0 0 5 5 1 0 0 0 0 | * * 2 *
... .oo3.xo3.ox3.oo&#x ♦ 0 10 10 | 0 0 0 30 30 30 | 0 0 0 0 10 20 0 30 30 20 10 | 0 0 0 0 0 5 5 0 10 20 10 5 5 | 0 0 0 0 0 1 0 5 5 1 | * * * 2
oxoo3ooxo oxoo3ooxo3ooox&#xt → all heights = sqrt(7/24) = 0.540062
(pt || (pseudo) tratet || (pseudo) gyro troct || dual tet)
o...3o... o...3o...3o... | 1 * * * ♦ 12 0 0 0 0 0 0 0 | 12 18 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 18 12 0 0 0 0 0 0 0 0 0 0 0 0 0 | 6 12 3 0 0 0 0 0 0 0 | 4 3 0 0
.o..3.o.. .o..3.o..3.o.. | * 12 * * ♦ 1 2 3 6 0 0 0 0 | 2 3 1 3 6 3 6 6 0 0 0 0 0 0 0 | 1 6 3 1 3 6 3 3 6 2 0 0 0 0 0 0 | 3 6 1 3 2 3 1 2 0 0 | 3 2 1 1
..o.3..o. ..o.3..o.3..o. | * * 18 * ♦ 0 0 0 4 2 4 2 0 | 0 0 0 0 2 4 2 8 1 2 2 4 4 1 0 | 0 1 0 0 2 4 2 8 2 2 1 2 2 2 2 0 | 1 2 0 4 2 4 4 2 1 1 | 2 1 2 2
...o3...o ...o3...o3...o | * * * 4 ♦ 0 0 0 0 0 0 9 3 | 0 0 0 0 0 0 0 0 0 0 0 9 9 9 3 | 0 0 0 0 0 0 0 9 0 0 0 3 9 3 9 1 | 0 0 0 3 0 3 9 0 3 3 | 1 0 3 3
-----------------------------+-----------+------------------------+-------------------------------------------+---------------------------------------------+--------------------------+--------
oo..3oo.. oo..3oo..3oo..&#x | 1 1 0 0 | 12 * * * * * * * | 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 6 1 0 0 0 0 0 0 0 | 3 2 0 0
.x.. .... .... .... .... | 0 2 0 0 | * 12 * * * * * * | 1 0 1 0 3 0 0 0 0 0 0 0 0 0 0 | 1 3 0 0 3 3 0 0 0 0 0 0 0 0 0 0 | 3 3 0 3 1 0 0 0 0 0 | 3 1 1 0
.... .... .x.. .... .... | 0 2 0 0 | * * 18 * * * * * | 0 1 0 2 0 0 2 0 0 0 0 0 0 0 0 | 0 2 2 1 0 0 1 0 4 0 0 0 0 0 0 0 | 1 4 1 0 0 2 0 2 0 0 | 2 2 0 1
.oo.3.oo. .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * 72 * * * * | 0 0 0 0 1 1 1 2 0 0 0 0 0 0 0 | 0 1 0 0 1 2 1 2 2 1 0 0 0 0 0 0 | 1 2 0 2 1 2 1 1 0 0 | 2 1 1 1
.... ..x. .... .... .... | 0 0 2 0 | * * * * 18 * * * | 0 0 0 0 0 2 0 0 1 0 0 2 0 0 0 | 0 0 0 0 2 0 1 4 0 0 0 2 1 0 0 0 | 1 0 0 4 0 2 2 0 1 0 | 2 0 2 1
.... .... .... ..x. .... | 0 0 2 0 | * * * * * 36 * * | 0 0 0 0 0 0 0 2 0 1 1 0 1 0 0 | 0 0 0 0 0 1 0 2 2 2 1 0 0 1 1 0 | 0 1 0 1 1 2 2 2 0 1 | 1 1 1 2
..oo3..oo ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * 36 * | 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 | 0 0 0 0 0 0 0 4 0 0 0 1 2 1 2 0 | 0 0 0 2 0 2 4 0 1 1 | 1 0 2 2
.... .... .... .... ...x | 0 0 0 2 | * * * * * * * 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 | 0 0 0 0 0 0 0 0 0 0 0 0 3 0 6 1 | 0 0 0 0 0 0 6 0 1 3 | 0 0 2 3
-----------------------------+-----------+------------------------+-------------------------------------------+---------------------------------------------+--------------------------+--------
ox.. .... .... .... ....&#x | 1 2 0 0 | 2 1 0 0 0 0 0 0 | 12 * * * * * * * * * * * * * * | 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 | 3 1 0 0
.... .... ox.. .... ....&#x | 1 2 0 0 | 2 0 1 0 0 0 0 0 | * 18 * * * * * * * * * * * * * | 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 4 1 0 0 0 0 0 0 0 | 2 2 0 0
.x..3.o.. .... .... .... | 0 3 0 0 | 0 3 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * * | 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 | 3 0 0 3 0 0 0 0 0 0 | 3 0 1 0
.... .... .x..3.o.. .... | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * * 12 * * * * * * * * * * * | 0 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 | 0 2 1 0 0 1 0 2 0 0 | 1 2 0 1
.xo. .... .... .... ....&#x | 0 2 1 0 | 0 1 0 2 0 0 0 0 | * * * * 36 * * * * * * * * * * | 0 1 0 0 1 2 0 0 0 0 0 0 0 0 0 0 | 1 2 0 2 1 0 0 0 0 0 | 2 1 1 0
.... .ox. .... .... ....&#x | 0 1 2 0 | 0 0 0 2 1 0 0 0 | * * * * * 36 * * * * * * * * * | 0 0 0 0 1 0 1 2 0 0 0 0 0 0 0 0 | 1 0 0 2 0 2 1 0 0 0 | 2 0 1 1
.... .... .xo. .... ....&#x | 0 2 1 0 | 0 0 1 2 0 0 0 0 | * * * * * * 36 * * * * * * * * | 0 1 0 0 0 0 1 0 2 0 0 0 0 0 0 0 | 1 2 0 0 0 2 0 1 0 0 | 2 1 0 1
.... .... .... .ox. ....&#x | 0 1 2 0 | 0 0 0 2 0 1 0 0 | * * * * * * * 72 * * * * * * * | 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 | 0 1 0 1 1 1 1 1 0 0 | 1 1 1 1
..o.3..x. .... .... .... | 0 0 3 0 | 0 0 0 0 3 0 0 0 | * * * * * * * * 6 * * * * * * | 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 | 1 0 0 4 0 0 0 0 1 0 | 2 0 2 0
.... .... ..o.3..x. .... | 0 0 3 0 | 0 0 0 0 0 3 0 0 | * * * * * * * * * 12 * * * * * | 0 0 0 0 0 0 0 0 2 0 1 0 0 1 0 0 | 0 1 0 0 0 2 0 2 0 1 | 1 1 0 2
.... .... .... ..x.3..o. | 0 0 3 0 | 0 0 0 0 0 3 0 0 | * * * * * * * * * * 12 * * * * | 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 | 0 0 0 0 1 0 2 2 0 1 | 0 1 1 2
.... ..xo .... .... ....&#x | 0 0 2 1 | 0 0 0 0 1 0 2 0 | * * * * * * * * * * * 36 * * * | 0 0 0 0 0 0 0 2 0 0 0 1 1 0 0 0 | 0 0 0 2 0 1 2 0 1 0 | 1 0 2 1
.... .... .... ..xo ....&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * 36 * * | 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 | 0 0 0 1 0 2 2 0 0 1 | 1 0 1 2
.... .... .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * 18 * | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 | 0 0 0 0 0 0 4 0 1 1 | 0 0 2 2
.... .... .... ...o3...x | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 | 0 0 0 0 0 0 3 0 0 3 | 0 0 1 3
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ox..3oo.. .... .... ....&#x ♦ 1 3 0 0 | 3 3 0 0 0 0 0 0 | 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * * | 3 0 0 0 0 0 0 0 0 0 | 3 0 0 0
oxo. .... oxo. .... ....&#xt ♦ 1 4 1 0 | 4 2 2 4 0 0 0 0 | 2 2 0 0 2 0 2 0 0 0 0 0 0 0 0 | * 18 * * * * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 | 2 1 0 0
.... .... ox..3oo.. ....&#x ♦ 1 3 0 0 | 3 0 3 0 0 0 0 0 | 0 3 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * 12 * * * * * * * * * * * * * | 0 2 1 0 0 0 0 0 0 0 | 1 2 0 0
.... .... .x..3.o..3.o.. ♦ 0 4 0 0 | 0 0 6 0 0 0 0 0 | 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 | * * * 3 * * * * * * * * * * * * | 0 0 1 0 0 0 0 2 0 0 | 0 2 0 1
.xo.3.ox. .... .... ....&#x ♦ 0 3 3 0 | 0 3 0 6 3 0 0 0 | 0 0 1 0 3 3 0 0 1 0 0 0 0 0 0 | * * * * 12 * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 2 0 1 0
.xo. .... .... .ox. ....&#x ♦ 0 2 2 0 | 0 1 0 4 0 1 0 0 | 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 | * * * * * 36 * * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 1 1 1 0
.... .ox. .xo. .... ....&#x ♦ 0 2 2 0 | 0 0 1 4 1 0 0 0 | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 | * * * * * * 18 * * * * * * * * * | 1 0 0 0 0 2 0 0 0 0 | 2 0 0 1
.... .oxo .... .oxo ....&#xt ♦ 0 1 4 1 | 0 0 0 4 2 2 4 0 | 0 0 0 0 0 2 0 2 0 0 0 2 2 0 0 | * * * * * * * 36 * * * * * * * * | 0 0 0 1 0 1 1 0 0 0 | 1 0 1 1
.... .... .xo.3.ox. ....&#x ♦ 0 3 3 0 | 0 0 3 6 0 3 0 0 | 0 0 0 1 0 0 3 3 0 1 0 0 0 0 0 | * * * * * * * * 24 * * * * * * * | 0 1 0 0 0 1 0 1 0 0 | 1 1 0 1
.... .... .... .ox.3.oo.&#x ♦ 0 1 3 0 | 0 0 0 3 0 3 0 0 | 0 0 0 0 0 0 0 3 0 0 1 0 0 0 0 | * * * * * * * * * 24 * * * * * * | 0 0 0 0 1 0 1 1 0 0 | 0 1 1 1
.... .... ..o.3..x.3..o. ♦ 0 0 6 0 | 0 0 0 0 0 12 0 0 | 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 | * * * * * * * * * * 3 * * * * * | 0 0 0 0 0 0 0 2 0 1 | 0 1 0 2
..oo3..xo .... .... ....&#x ♦ 0 0 3 1 | 0 0 0 0 3 0 3 0 | 0 0 0 0 0 0 0 0 1 0 0 3 0 0 0 | * * * * * * * * * * * 12 * * * * | 0 0 0 2 0 0 0 0 1 0 | 1 0 2 0
.... ..xo .... .... ..ox&#x ♦ 0 0 2 2 | 0 0 0 0 1 0 4 1 | 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 | * * * * * * * * * * * * 18 * * * | 0 0 0 0 0 0 2 0 1 0 | 0 0 2 1
.... .... ..oo3..xo ....&#x ♦ 0 0 3 1 | 0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 | * * * * * * * * * * * * * 12 * * | 0 0 0 0 0 2 0 0 0 1 | 1 0 0 2
.... .... .... ..xo3..ox&#x ♦ 0 0 3 3 | 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 0 0 0 0 1 0 3 3 1 | * * * * * * * * * * * * * * 12 * | 0 0 0 0 0 0 2 0 0 1 | 0 0 1 2
.... .... ...o3...o3...x ♦ 0 0 0 4 | 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 3 | 0 0 0 3
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oxo.3oox. oxo. .... ....&#xt ♦ 1 6 3 0 | 6 6 3 12 3 0 0 0 | 6 3 2 0 6 6 6 0 1 0 0 0 0 0 0 | 2 3 0 0 2 0 3 0 0 0 0 0 0 0 0 0 | 6 * * * * * * * * * | 2 0 0 0
oxo. .... oxo.3oox. ....&#xt ♦ 1 6 3 0 | 6 3 6 12 0 3 0 0 | 3 6 0 2 6 0 6 6 0 1 0 0 0 0 0 | 0 3 2 0 0 3 0 0 2 0 0 0 0 0 0 0 | * 12 * * * * * * * * | 1 1 0 0
.... .... ox..3oo..3oo..&#x ♦ 1 4 0 0 | 4 0 6 0 0 0 0 0 | 0 6 0 4 0 0 0 0 0 0 0 0 0 0 0 | 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * | 0 2 0 0
.xoo3.oxo .... .oxo ....&#xt ♦ 0 3 6 1 | 0 3 0 12 6 3 6 0 | 0 0 1 0 6 6 0 6 2 0 0 6 3 0 0 | 0 0 0 0 2 3 0 3 0 0 0 2 0 0 0 0 | * * * 12 * * * * * * | 1 0 1 0
.xo. .... .... .ox.3.oo.&#x ♦ 0 2 3 0 | 0 1 0 6 0 3 0 0 | 0 0 0 0 3 0 0 6 0 0 1 0 0 0 0 | 0 0 0 0 0 3 0 0 0 2 0 0 0 0 0 0 | * * * * 12 * * * * * | 0 1 1 0
.... .oxo .xoo3.oxo ....&#xt ♦ 0 3 6 1 | 0 0 3 12 3 6 6 0 | 0 0 0 1 0 6 6 6 0 2 0 3 6 0 0 | 0 0 0 0 0 0 3 3 2 0 0 0 0 2 0 0 | * * * * * 12 * * * * | 1 0 0 1
.... .oxo .... .oxo3.oox&#xt ♦ 0 1 6 3 | 0 0 0 6 3 6 12 3 | 0 0 0 0 0 3 0 6 0 0 2 6 6 6 1 | 0 0 0 0 0 0 0 3 0 2 0 0 3 0 2 0 | * * * * * * 12 * * * | 0 0 1 1
.... .... .xo.3.ox.3.oo.&#x ♦ 0 4 6 0 | 0 0 6 12 0 12 0 0 | 0 0 0 4 0 0 6 12 0 4 4 0 0 0 0 | 0 0 0 1 0 0 0 0 4 4 1 0 0 0 0 0 | * * * * * * * 6 * * | 0 1 0 1
..oo3..xo .... .... ..ox&#x ♦ 0 0 3 2 | 0 0 0 0 3 0 6 1 | 0 0 0 0 0 0 0 0 1 0 0 6 0 3 0 | 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0 | * * * * * * * * 6 * | 0 0 2 0
.... .... ..oo3..xo3..ox&#x ♦ 0 0 6 4 | 0 0 0 0 0 12 12 6 | 0 0 0 0 0 0 0 0 0 4 4 0 12 6 4 | 0 0 0 0 0 0 0 0 0 0 1 0 0 4 4 1 | * * * * * * * * * 3 | 0 0 0 2
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oxoo3ooxo oxoo3ooxo ....&#xt ♦ 1 9 9 1 | 9 9 9 36 9 9 9 0 | 9 9 3 3 18 18 18 18 3 3 0 9 9 0 0 | 3 9 3 0 6 9 9 9 6 0 0 3 0 3 0 0 | 3 3 0 3 0 3 0 0 0 0 | 4 * * *
oxo. .... oxo.3oox.3ooo.&#xt ♦ 1 8 6 0 | 8 4 12 24 0 12 0 0 | 4 12 0 8 12 0 12 24 0 4 4 0 0 0 0 | 0 6 8 2 0 12 0 0 8 8 1 0 0 0 0 0 | 0 4 2 0 4 0 0 2 0 0 | * 3 * *
.xoo3.oxo .... .oxo3.oox&#xt ♦ 0 3 9 3 | 0 3 0 18 9 9 18 3 | 0 0 1 0 9 9 0 18 3 0 3 18 9 9 1 | 0 0 0 0 3 9 0 9 0 6 0 6 9 0 3 0 | 0 0 0 3 3 0 3 0 3 0 | * * 4 *
.... .oxo .xoo3.oxo3.oox&#xt ♦ 0 4 12 4 | 0 0 6 24 6 24 24 6 | 0 0 0 4 0 12 12 24 0 8 8 12 24 12 4 | 0 0 0 1 0 0 6 12 8 8 2 0 6 8 8 1 | 0 0 0 0 0 4 4 2 0 2 | * * * 3