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Acronym
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brox (old: drax)
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Name
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birectified hexeract,
Gosset polytope 03,1,1,
equatorial cross-section of brag-first sez
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Circumradius
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sqrt(2) = 1.414214
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Inradius
wrt. rix
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2/sqrt(3) = 1.154701
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Inradius
wrt. nit
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1/sqrt(2) = 0.707107
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Lace city
in approx. ASCII-art
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 ©
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o3x3o4o o3o3x4o o3x3o4o -- o3o3x3o4o (nit)
(ico) (rit)
o3o3x4o o3o3o4q o3o3x4o -- o3o3o3x4o (rin)
(q-tes)
o3x3o4o o3o3x4o o3x3o4o -- o3o3x3o4o (nit)
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o3x3o3o x3o3x3o o3x3o3x o3o3x3o -- o3o3x3o4o (nit)
(rap) (srip)
x3o3o3o x3x3o3o o3x3x3o o3o3x3x o3o3o3x -- o3o3o3x4o (rin)
(pen) (tip) (deca)
o3x3o3o x3o3x3o o3x3o3x o3o3x3o -- o3o3x3o4o (nit)
\ \ \ \ \
\ \ \ \ +-- o3x3o3o3o (rix)
\ \ \ +----------- x3o3x3o3o (sarx)
\ \ +-------------------- o3x3o3x3o (sibrid)
\ +----------------------------- o3o3x3o3x (inv sarx)
+-------------------------------------- o3o3o3x3o (dual rix)
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Lace hyper city
in approx. ASCII-art
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o4o x4o o4o
x4o o4q x4o
o4o x4o o4o
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x4o o4q x4o
o4q o4q
x4o o4q x4o
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o4o x4o o4o
x4o o4q x4o
o4o x4o o4o
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x4o o4q x4o
o4q o4q
x4o o4q x4o
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o4q o4q
o4q o4q
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x4o o4q x4o
o4q o4q
x4o o4q x4o
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o4o x4o o4o
x4o o4q x4o
o4o x4o o4o
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x4o o4q x4o
o4q o4q
x4o o4q x4o
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o4o x4o o4o
x4o o4q x4o
o4o x4o o4o
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Coordinates
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(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0) & all permutations, all changes of sign
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Volume
|
331/45 = 14.711111
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Surface
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122 sqrt(2)/3 = 57.511352
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Dihedral angles
(at margins)
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- at pen between rix and rix: arccos(-2/3) = 131.810315°
- at rap between nit and rix: arccos[-1/sqrt(6)] = 114.094843°
- at ico between nit and nit: 90°
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Face vector
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240, 1920, 3200, 2080, 636, 76
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Confer
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- related segmentoexa:
-
nitarin
rixasarx
sarxasibrid
- related scaliform:
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codibrox
- ambification:
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saborx
- ambification pre-image:
-
hax
- general polytopal classes:
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Wythoffian polypeta
lace simplices
Coxeter-Elte-Gosset polytopes
- analogs:
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birectified hypercube brCn
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External
links
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Incidence matrix according to Dynkin symbol
o3o3o3x3o4o
. . . . . . | 240 ♦ 16 | 24 16 | 16 24 4 | 4 16 6 | 4 4
------------+-----+------+-----------+-------------+------------+------
. . . x . . | 2 | 1920 | 3 2 | 3 6 1 | 1 6 3 | 2 3
------------+-----+------+-----------+-------------+------------+------
. . o3x . . | 3 | 3 | 1920 * | 2 2 0 | 1 4 1 | 2 2
. . . x3o . | 3 | 3 | * 1280 | 0 3 1 | 0 3 3 | 1 3
------------+-----+------+-----------+-------------+------------+------
. o3o3x . . ♦ 4 | 6 | 4 0 | 960 * * | 1 2 0 | 2 1
. . o3x3o . ♦ 6 | 12 | 4 4 | * 960 * | 0 2 1 | 1 2
. . . x3o4o ♦ 6 | 12 | 0 8 | * * 160 | 0 0 3 | 0 3
------------+-----+------+-----------+-------------+------------+------
o3o3o3x . . ♦ 5 | 10 | 10 0 | 5 0 0 | 192 * * | 2 0
. o3o3x3o . ♦ 10 | 30 | 20 10 | 5 5 0 | * 384 * | 1 1
. . o3x3o4o ♦ 24 | 96 | 32 64 | 0 16 8 | * * 60 | 0 2
------------+-----+------+-----------+-------------+------------+------
o3o3o3x3o . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 | 64 *
. o3o3x3o4o ♦ 80 | 480 | 320 320 | 80 160 40 | 0 32 10 | * 12
o3o3o3x3o4/3o
. . . . . . | 240 ♦ 16 | 24 16 | 16 24 4 | 4 16 6 | 4 4
--------------+-----+------+-----------+-------------+------------+------
. . . x . . | 2 | 1920 | 3 2 | 3 6 1 | 1 6 3 | 2 3
--------------+-----+------+-----------+-------------+------------+------
. . o3x . . | 3 | 3 | 1920 * | 2 2 0 | 1 4 1 | 2 2
. . . x3o . | 3 | 3 | * 1280 | 0 3 1 | 0 3 3 | 1 3
--------------+-----+------+-----------+-------------+------------+------
. o3o3x . . ♦ 4 | 6 | 4 0 | 960 * * | 1 2 0 | 2 1
. . o3x3o . ♦ 6 | 12 | 4 4 | * 960 * | 0 2 1 | 1 2
. . . x3o4/3o ♦ 6 | 12 | 0 8 | * * 160 | 0 0 3 | 0 3
--------------+-----+------+-----------+-------------+------------+------
o3o3o3x . . ♦ 5 | 10 | 10 0 | 5 0 0 | 192 * * | 2 0
. o3o3x3o . ♦ 10 | 30 | 20 10 | 5 5 0 | * 384 * | 1 1
. . o3x3o4/3o ♦ 24 | 96 | 32 64 | 0 16 8 | * * 60 | 0 2
--------------+-----+------+-----------+-------------+------------+------
o3o3o3x3o . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 | 64 *
. o3o3x3o4/3o ♦ 80 | 480 | 320 320 | 80 160 40 | 0 32 10 | * 12
o3x3o *b3o3o3o
. . . . . . | 240 ♦ 16 | 8 8 24 | 4 12 12 16 | 6 8 8 4 | 4 2 2
---------------+-----+------+--------------+-----------------+----------------+---------
. x . . . . | 2 | 1920 | 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1
---------------+-----+------+--------------+-----------------+----------------+---------
o3x . . . . | 3 | 3 | 640 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0
. x3o . . . | 3 | 3 | * 640 * | 1 0 3 0 | 3 0 3 0 | 3 0 1
. x . *b3o . . | 3 | 3 | * * 1920 | 0 1 1 2 | 1 2 2 1 | 2 1 1
---------------+-----+------+--------------+-----------------+----------------+---------
o3x3o . . . ♦ 6 | 12 | 4 4 0 | 160 * * * | 3 0 0 0 | 3 0 0
o3x . *b3o . . ♦ 6 | 12 | 4 0 4 | * 480 * * | 1 2 0 0 | 2 1 0
. x3o *b3o . . ♦ 6 | 12 | 0 4 4 | * * 480 * | 1 0 2 0 | 2 0 1
. x . *b3o3o . ♦ 4 | 6 | 0 0 4 | * * * 960 | 0 1 1 1 | 1 1 1
---------------+-----+------+--------------+-----------------+----------------+---------
o3x3o *b3o . . ♦ 24 | 96 | 32 32 32 | 8 8 8 0 | 60 * * * | 2 0 0
o3x . *b3o3o . ♦ 10 | 30 | 10 0 20 | 0 5 0 5 | * 192 * * | 1 1 0
. x3o *b3o3o . ♦ 10 | 30 | 0 10 20 | 0 0 5 5 | * * 192 * | 1 0 1
. x . *b3o3o3o ♦ 5 | 10 | 0 0 10 | 0 0 0 5 | * * * 192 | 0 1 1
---------------+-----+------+--------------+-----------------+----------------+---------
o3x3o *b3o3o . ♦ 80 | 480 | 160 160 320 | 40 80 80 80 | 10 16 16 0 | 12 * *
o3x . *b3o3o3o ♦ 15 | 60 | 20 0 60 | 0 15 0 30 | 0 6 0 6 | * 32 *
. x3o *b3o3o3o ♦ 15 | 60 | 0 20 60 | 0 0 15 30 | 0 0 6 6 | * * 32
ooo3ooo3xox3oxo4ooo&#xt → both heights = 1/sqrt(2) = 0.707107
(nit || pseudo rin || nit)
o..3o..3o..3o..4o.. & | 160 * ♦ 12 4 0 | 12 12 12 4 0 | 4 12 3 12 12 1 0 | 4 3 4 12 3 0 | 1 4 3
.o.3.o.3.o.3.o.4.o. | * 80 ♦ 0 8 8 | 0 0 12 16 12 | 0 0 0 8 24 4 8 | 0 0 2 16 6 2 | 0 4 4
--------------------------+--------+-------------+---------------------+---------------------------+---------------------+--------
... ... x.. ... ... & | 2 0 | 960 * * | 2 2 1 0 0 | 1 4 1 2 2 0 0 | 2 2 1 4 1 0 | 1 2 2
oo.3oo.3oo.3oo.4oo.&#x & | 1 1 | * 640 * | 0 0 3 2 0 | 0 0 0 3 6 1 0 | 0 0 1 6 3 0 | 0 2 3
... ... ... .x. ... | 0 2 | * * 320 | 0 0 0 2 3 | 0 0 0 0 6 1 3 | 0 0 0 6 3 1 | 0 2 3
--------------------------+--------+-------------+---------------------+---------------------------+---------------------+--------
... o..3x.. ... ... & | 3 0 | 3 0 0 | 640 * * * * | 1 2 0 1 0 0 0 | 2 1 1 2 0 0 | 1 2 1
... ... x..3o.. ... & | 3 0 | 3 0 0 | * 640 * * * | 0 2 1 0 1 0 0 | 1 2 0 2 1 0 | 1 1 2
... ... xo. ... ...&#x & | 2 1 | 1 2 0 | * * 960 * * | 0 0 0 2 2 0 0 | 0 0 1 4 1 0 | 0 2 2
... ... ... ox. ...&#x & | 1 2 | 0 2 1 | * * * 640 * | 0 0 0 0 3 1 0 | 0 0 0 3 3 0 | 0 1 3
... ... .o.3.x. ... | 0 3 | 0 0 3 | * * * * 320 | 0 0 0 0 2 0 2 | 0 0 0 4 1 1 | 0 2 2
--------------------------+--------+-------------+---------------------+---------------------------+---------------------+--------
o..3o..3x.. ... ... & ♦ 4 0 | 6 0 0 | 4 0 0 0 0 | 160 * * * * * * | 2 0 1 0 0 0 | 1 2 0
... o..3x..3o.. ... & ♦ 6 0 | 12 0 0 | 4 4 0 0 0 | * 320 * * * * * | 1 1 0 1 0 0 | 1 1 1
... ... x..3o..4o.. & ♦ 6 0 | 12 0 0 | 0 8 0 0 0 | * * 80 * * * * | 0 2 0 0 1 0 | 1 0 2
... oo.3xo. ... ...&#x & ♦ 3 1 | 3 3 0 | 1 0 3 0 0 | * * * 640 * * * | 0 0 1 2 0 0 | 0 2 1
... ... xo.3ox. ...&#x & ♦ 3 3 | 3 6 3 | 0 1 3 3 1 | * * * * 640 * * | 0 0 0 2 1 0 | 0 1 2
... ... ... oxo4ooo&#xt ♦ 2 4 | 0 8 4 | 0 0 0 8 0 | * * * * * 80 * | 0 0 0 0 3 0 | 0 0 3
... .o.3.o.3.x. ... ♦ 0 4 | 0 0 6 | 0 0 0 0 4 | * * * * * * 160 | 0 0 0 2 0 1 | 0 2 1
--------------------------+--------+-------------+---------------------+---------------------------+---------------------+--------
o..3o..3x..3o.. ... & ♦ 10 0 | 30 0 0 | 20 10 0 0 0 | 5 5 0 0 0 0 0 | 64 * * * * * | 1 1 0
... o..3x..3o..4o.. & ♦ 24 0 | 96 0 0 | 32 64 0 0 0 | 0 16 8 0 0 0 0 | * 20 * * * * | 1 0 1
oo.3oo.3xo. ... ...&#x & ♦ 4 1 | 6 4 0 | 4 0 6 0 0 | 1 0 0 4 0 0 0 | * * 160 * * * | 0 2 0
... oo.3xo.3ox. ...&#x & ♦ 6 4 | 12 12 6 | 4 4 12 6 4 | 0 1 0 4 4 0 1 | * * * 320 * * | 0 1 1
... ... xox3oxo4ooo&#xt ♦ 12 12 | 24 48 24 | 0 16 24 48 8 | 0 0 2 0 16 6 0 | * * * * 40 * | 0 0 2
.o.3.o.3.o.3.x. ... ♦ 0 5 | 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * 32 | 0 2 0
--------------------------+--------+-------------+---------------------+---------------------------+---------------------+--------
o..3o..3x..3o..4o.. & ♦ 80 0 | 480 0 0 | 320 320 0 0 0 | 80 160 40 0 0 0 0 | 32 10 0 0 0 0 | 2 * *
oo.3oo.3xo.3ox. ...&#x & ♦ 10 5 | 30 20 10 | 20 10 30 10 10 | 5 5 0 20 10 0 5 | 1 0 5 5 0 1 | * 64 *
... ooo3xox3oxo4ooo&#xt ♦ 48 32 | 192 192 96 | 64 128 192 192 64 | 0 32 16 64 128 24 16 | 0 2 0 32 8 0 | * * 10
oxo3xox3oxo *b3ooo3ooo&#x → both heights = 1/sqrt(2) = 0.707107
(nit || pseudo rin || nit)
o..3o..3o.. *b3o..3o.. & | 160 * ♦ 12 4 0 0 | 6 6 12 2 12 2 0 0 | 3 6 6 4 6 1 6 12 0 0 | 3 2 2 3 6 6 4 0 0 | 1 3 2 2
.o.3.o.3.o. *b3.o.3.o. | * 80 ♦ 0 8 4 4 | 0 0 0 8 12 8 6 6 | 0 0 0 0 12 4 12 8 4 4 | 0 0 0 6 8 8 2 1 1 | 0 4 2 2
-----------------------------+--------+-----------------+---------------------------------+-------------------------------------+-------------------------------+-----------
... x.. ... ... ... & | 2 0 | 960 * * * | 1 1 2 0 1 0 0 0 | 1 2 2 1 1 0 1 2 0 0 | 2 1 1 1 2 2 1 0 0 | 1 2 1 1
oo.3oo.3oo. *b3oo.3oo.&#x & | 1 1 | * 640 * * | 0 0 0 1 3 1 0 0 | 0 0 0 0 3 1 3 3 0 0 | 0 0 0 3 3 3 1 0 0 | 0 3 1 1
.x. ... ... ... ... | 0 2 | * * 160 * | 0 0 0 2 0 0 3 0 | 0 0 0 0 6 1 0 0 3 0 | 0 0 0 3 6 0 0 1 0 | 0 3 2 0
... ... .x. ... ... | 0 2 | * * * 160 | 0 0 0 0 0 2 0 3 | 0 0 0 0 0 1 6 0 0 3 | 0 0 0 3 0 6 0 0 1 | 0 3 0 2
-----------------------------+--------+-----------------+---------------------------------+-------------------------------------+-------------------------------+-----------
o..3x.. ... ... ... & | 3 0 | 3 0 0 0 | 320 * * * * * * * | 1 2 0 0 1 0 0 0 0 0 | 2 1 0 1 2 0 0 0 0 | 1 2 1 0
... x..3o.. ... ... & | 3 0 | 3 0 0 0 | * 320 * * * * * * | 1 0 2 0 0 0 1 0 0 0 | 2 0 1 1 0 2 0 0 0 | 1 2 0 1
... x.. ... *b3o.. ... & | 3 0 | 3 0 0 0 | * * 640 * * * * * | 0 1 1 1 0 0 0 1 0 0 | 1 1 1 0 1 1 1 0 0 | 1 1 1 1
ox. ... ... ... ...&#x & | 1 2 | 0 2 1 0 | * * * 320 * * * * | 0 0 0 0 3 1 0 0 0 0 | 0 0 0 3 3 0 0 0 0 | 0 3 1 0
... xo. ... ... ...&#x & | 2 1 | 1 2 0 0 | * * * * 960 * * * | 0 0 0 0 1 0 1 2 0 0 | 0 0 0 1 2 2 1 0 0 | 0 2 1 1
... ... ox. ... ...&#x & | 1 2 | 0 2 0 1 | * * * * * 320 * * | 0 0 0 0 0 1 3 0 0 0 | 0 0 0 3 0 3 0 0 0 | 0 3 0 1
.x.3.o. ... ... ... | 0 3 | 0 0 3 0 | * * * * * * 160 * | 0 0 0 0 2 0 0 0 2 0 | 0 0 0 1 4 0 0 1 0 | 0 2 2 0
... .o.3.x. ... ... | 0 3 | 0 0 0 3 | * * * * * * * 160 | 0 0 0 0 0 0 2 0 0 2 | 0 0 0 1 0 4 0 0 1 | 0 2 0 2
-----------------------------+--------+-----------------+---------------------------------+-------------------------------------+-------------------------------+-----------
o..3x..3o.. ... ... & ♦ 6 0 | 12 0 0 0 | 4 4 0 0 0 0 0 0 | 80 * * * * * * * * * | 2 0 0 1 0 0 0 0 0 | 1 2 0 0
o..3x.. ... *b3o.. ... & ♦ 6 0 | 12 0 0 0 | 4 0 4 0 0 0 0 0 | * 160 * * * * * * * * | 1 1 0 0 1 0 0 0 0 | 1 1 1 0
... x..3o.. *b3o.. ... & ♦ 6 0 | 12 0 0 0 | 0 4 4 0 0 0 0 0 | * * 160 * * * * * * * | 1 0 1 0 0 1 0 0 0 | 1 1 0 1
... x.. ... *b3o..3o.. & ♦ 4 0 | 6 0 0 0 | 0 0 4 0 0 0 0 0 | * * * 160 * * * * * * | 0 1 1 0 0 0 1 0 0 | 1 0 1 1
ox.3xo. ... ... ...&#x & ♦ 3 3 | 3 6 3 0 | 1 0 0 3 3 0 1 0 | * * * * 320 * * * * * | 0 0 0 1 2 0 0 0 0 | 0 2 1 0
oxo ... oxo ... ...&#xt ♦ 2 4 | 0 8 2 2 | 0 0 0 4 0 4 0 0 | * * * * * 80 * * * * | 0 0 0 3 0 0 0 0 0 | 0 3 0 0
... xo.3ox. ... ...&#x & ♦ 3 3 | 3 6 0 3 | 0 1 0 0 3 3 0 1 | * * * * * * 320 * * * | 0 0 0 1 0 2 0 0 0 | 0 2 0 1
... xo. ... *b3oo. ...&#x & ♦ 3 1 | 3 3 0 0 | 0 0 1 0 3 0 0 0 | * * * * * * * 640 * * | 0 0 0 0 1 1 1 0 0 | 0 1 1 1
.x.3.o. ... *b3.o. ... ♦ 0 4 | 0 0 6 0 | 0 0 0 0 0 0 4 0 | * * * * * * * * 80 * | 0 0 0 0 2 0 0 1 0 | 0 1 2 0
... .o.3.x. *b3.o. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 0 0 4 | * * * * * * * * * 80 | 0 0 0 0 0 2 0 0 1 | 0 1 0 2
-----------------------------+--------+-----------------+---------------------------------+-------------------------------------+-------------------------------+-----------
o..3x..3o.. *b3o.. ... & ♦ 24 0 | 96 0 0 0 | 32 32 32 0 0 0 0 0 | 8 8 8 0 0 0 0 0 0 0 | 20 * * * * * * * * | 1 1 0 0
o..3x.. ... *b3o..3o.. & ♦ 10 0 | 30 0 0 0 | 10 0 20 0 0 0 0 0 | 0 5 0 5 0 0 0 0 0 0 | * 32 * * * * * * * | 1 0 1 0
... x..3o.. *b3o..3o.. & ♦ 10 0 | 30 0 0 0 | 0 10 20 0 0 0 0 0 | 0 0 5 5 0 0 0 0 0 0 | * * 32 * * * * * * | 1 0 0 1
oxo3xox3oxo ... ...&#xt ♦ 12 12 | 24 48 12 12 | 8 8 0 24 24 24 4 4 | 2 0 0 0 8 6 8 0 0 0 | * * * 40 * * * * * | 0 2 0 0
ox.3xo. ... *b3oo. ...&#x & ♦ 6 4 | 12 12 6 0 | 4 0 4 6 12 0 4 0 | 0 1 0 0 4 0 0 4 1 0 | * * * * 160 * * * * | 0 1 1 0
... xo.3ox. *b3oo. ...&#x & ♦ 6 4 | 12 12 0 6 | 0 4 4 0 12 6 0 4 | 0 0 1 0 0 0 4 4 0 1 | * * * * * 160 * * * | 0 1 0 1
... xo. ... *b3oo.3oo.&#x & ♦ 4 1 | 6 4 0 0 | 0 0 4 0 6 0 0 0 | 0 0 0 1 0 0 0 4 0 0 | * * * * * * 160 * * | 0 0 1 1
.x.3.o. ... *b3.o.3.o. ♦ 0 5 | 0 0 10 0 | 0 0 0 0 0 0 10 0 | 0 0 0 0 0 0 0 0 5 0 | * * * * * * * 16 * | 0 0 2 0
... .o.3.x. *b3.o.3.o. ♦ 0 5 | 0 0 0 10 | 0 0 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 5 | * * * * * * * * 16 | 0 0 0 2
-----------------------------+--------+-----------------+---------------------------------+-------------------------------------+-------------------------------+-----------
o..3x..3o.. *b3o..3o.. & ♦ 80 0 | 480 0 0 0 | 160 160 320 0 0 0 0 0 | 40 80 80 80 0 0 0 0 0 0 | 10 16 16 0 0 0 0 0 0 | 2 * * *
oxo3xox3oxo *b3ooo ...&#xt ♦ 48 32 | 192 192 48 48 | 64 64 64 96 192 96 32 32 | 16 16 16 0 64 24 64 64 8 8 | 2 0 0 8 16 16 0 0 0 | * 10 * *
ox.3xo. ... *b3oo.3oo.&#x & ♦ 10 5 | 30 20 10 0 | 10 0 20 10 30 0 10 0 | 0 5 0 5 10 0 0 20 5 0 | 0 1 0 0 5 0 5 1 0 | * * 32 *
... xo.3ox. *b3oo.3oo.&#x & ♦ 10 5 | 30 20 0 10 | 0 10 20 0 30 10 0 10 | 0 0 5 5 0 0 10 20 0 5 | 0 0 1 0 0 5 5 0 1 | * * * 32
oxooo3xoxoo3oxoxo3ooxox3oooxo&#xt → all heights = 1/sqrt(3) = 0.577350
(rix || pseudo sarx || pseudo sibrid || pseudo inv sarx || inv rix)
o....3o....3o....3o....3o.... & | 30 * * ♦ 8 8 0 0 0 0 | 4 12 4 8 12 0 0 0 0 0 0 0 0 0 | 6 8 4 6 12 8 0 0 0 0 0 0 0 0 0 | 4 2 6 4 8 2 0 0 0 0 0 | 1 4 1 2 0
.o...3.o...3.o...3.o...3.o... & | * 120 * ♦ 0 2 2 6 6 0 | 0 0 2 1 6 1 3 6 6 3 6 6 0 0 | 0 0 1 6 3 6 3 2 3 6 3 3 6 2 0 | 0 0 3 6 3 2 1 4 2 3 2 | 0 4 2 1 1
..o..3..o..3..o..3..o..3..o.. | * * 90 ♦ 0 0 0 0 8 8 | 0 0 0 0 0 0 0 0 4 8 4 16 4 4 | 0 0 0 2 0 0 0 0 4 8 4 8 8 8 2 | 0 0 2 4 0 0 0 8 4 4 4 | 0 4 2 0 2
------------------------------------+-----------+-------------------------+-------------------------------------------------------+-------------------------------------------------------+-------------------------------------+--------------
..... x.... ..... ..... ..... & | 2 0 0 | 120 * * * * * | 1 3 0 1 0 0 0 0 0 0 0 0 0 0 | 3 3 1 0 3 0 0 0 0 0 0 0 0 0 0 | 3 1 3 0 3 0 0 0 0 0 0 | 1 3 0 1 0
oo...3oo...3oo...3oo...3oo...&#x & | 1 1 0 | * 240 * * * * | 0 0 1 1 3 0 0 0 0 0 0 0 0 0 | 0 0 1 3 3 3 0 0 0 0 0 0 0 0 0 | 0 0 3 3 3 1 0 0 0 0 0 | 0 3 1 1 0
.x... ..... ..... ..... ..... & | 0 2 0 | * * 120 * * * | 0 0 1 0 0 1 0 0 3 0 0 0 0 0 | 0 0 1 3 0 0 0 0 3 3 0 0 0 0 0 | 0 0 3 3 0 0 0 3 1 0 0 | 0 3 1 0 1
..... ..... .x... ..... ..... & | 0 2 0 | * * * 360 * * | 0 0 0 0 1 0 1 2 0 0 1 0 0 0 | 0 0 0 1 1 2 2 1 0 0 1 0 2 0 0 | 0 0 1 2 2 1 1 0 0 2 1 | 0 3 1 1 0
.oo..3.oo..3.oo..3.oo..3.oo..&#x & | 0 1 1 | * * * * 720 * | 0 0 0 0 0 0 0 0 1 1 1 2 0 0 | 0 0 0 1 0 0 0 0 1 2 1 2 2 1 0 | 0 0 1 2 0 0 0 3 1 2 1 | 0 3 1 0 1
..... ..x.. ..... ..... ..... & | 0 0 2 | * * * * * 360 | 0 0 0 0 0 0 0 0 0 1 0 2 1 1 | 0 0 0 0 0 0 0 0 1 1 1 2 2 2 1 | 0 0 1 1 0 0 0 3 1 2 2 | 0 3 1 0 1
------------------------------------+-----------+-------------------------+-------------------------------------------------------+-------------------------------------------------------+-------------------------------------+--------------
o....3x.... ..... ..... ..... & | 3 0 0 | 3 0 0 0 0 0 | 40 * * * * * * * * * * * * * | 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 3 0 3 0 0 0 0 0 0 0 0 | 1 3 0 0 0
..... x....3o.... ..... ..... & | 3 0 0 | 3 0 0 0 0 0 | * 120 * * * * * * * * * * * * | 1 2 0 0 1 0 0 0 0 0 0 0 0 0 0 | 2 1 1 0 2 0 0 0 0 0 0 | 1 2 0 1 0
ox... ..... ..... ..... .....&#x & | 1 2 0 | 0 2 1 0 0 0 | * * 120 * * * * * * * * * * * | 0 0 1 3 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
..... xo... ..... ..... .....&#x & | 2 1 0 | 1 2 0 0 0 0 | * * * 120 * * * * * * * * * * | 0 0 1 0 3 0 0 0 0 0 0 0 0 0 0 | 0 0 3 0 3 0 0 0 0 0 0 | 0 3 0 1 0
..... ..... ox... ..... .....&#x & | 1 2 0 | 0 2 0 1 0 0 | * * * * 360 * * * * * * * * * | 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 | 0 0 1 2 2 1 0 0 0 0 0 | 0 2 1 1 0
.x...3.o... ..... ..... ..... & | 0 3 0 | 0 0 3 0 0 0 | * * * * * 40 * * * * * * * * | 0 0 1 0 0 0 0 0 3 0 0 0 0 0 0 | 0 0 3 0 0 0 0 3 0 0 0 | 0 3 0 0 1
..... .o...3.x... ..... ..... & | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 120 * * * * * * * | 0 0 0 0 1 0 2 0 0 0 1 0 0 0 0 | 0 0 1 0 2 0 1 0 0 2 0 | 0 3 0 1 0
..... ..... .x...3.o... ..... & | 0 3 0 | 0 0 0 3 0 0 | * * * * * * * 240 * * * * * * | 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 | 0 0 0 1 1 1 1 0 0 1 1 | 0 2 1 1 0
.xo.. ..... ..... ..... .....&#x & | 0 2 1 | 0 0 1 0 2 0 | * * * * * * * * 360 * * * * * | 0 0 0 1 0 0 0 0 1 2 0 0 0 0 0 | 0 0 1 2 0 0 0 2 1 0 0 | 0 2 1 0 1
..... .ox.. ..... ..... .....&#x & | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * * * 360 * * * * | 0 0 0 0 0 0 0 0 1 0 1 2 0 0 0 | 0 0 1 0 0 0 0 3 0 2 0 | 0 3 0 0 1
..... ..... .xo.. ..... .....&#x & | 0 2 1 | 0 0 0 1 2 0 | * * * * * * * * * * 360 * * * | 0 0 0 1 0 0 0 0 0 0 1 0 2 0 0 | 0 0 1 2 0 0 0 0 0 2 1 | 0 3 1 0 0
..... ..... ..... .ox.. .....&#x & | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * * * * * 720 * * | 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 | 0 0 0 1 0 0 0 2 1 1 1 | 0 2 1 0 1
..o..3..x.. ..... ..... ..... & | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * * * 120 * | 0 0 0 0 0 0 0 0 1 0 0 0 0 2 1 | 0 0 1 0 0 0 0 2 1 0 2 | 0 2 1 0 1
..... ..x..3..o.. ..... ..... & | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * * * * 120 | 0 0 0 0 0 0 0 0 0 0 1 0 2 0 1 | 0 0 1 1 0 0 0 0 0 2 2 | 0 3 1 0 0
------------------------------------+-----------+-------------------------+-------------------------------------------------------+-------------------------------------------------------+-------------------------------------+--------------
o....3x....3o.... ..... ..... & ♦ 6 0 0 | 12 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 0 | 30 * * * * * * * * * * * * * * | 2 0 1 0 0 0 0 0 0 0 0 | 1 2 0 0 0
..... x....3o....3o.... ..... & ♦ 4 0 0 | 6 0 0 0 0 0 | 0 4 0 0 0 0 0 0 0 0 0 0 0 0 | * 60 * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 | 1 1 0 1 0
ox...3xo... ..... ..... .....&#x & ♦ 3 3 0 | 3 6 3 0 0 0 | 1 0 3 3 0 1 0 0 0 0 0 0 0 0 | * * 40 * * * * * * * * * * * * | 0 0 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 2 0 2 0 0 0 2 0 2 0 0 0 | * * * 180 * * * * * * * * * * * | 0 0 1 2 0 0 0 0 0 0 0 | 0 2 1 0 0
..... xo...3ox... ..... .....&#x & ♦ 3 3 0 | 3 6 0 3 0 0 | 0 1 0 3 3 0 1 0 0 0 0 0 0 0 | * * * * 120 * * * * * * * * * * | 0 0 1 0 2 0 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 0 3 0 0 1 0 0 0 0 0 0 | * * * * * 240 * * * * * * * * * | 0 0 0 1 1 1 0 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 0 0 4 4 0 0 0 0 0 0 | * * * * * * 60 * * * * * * * * | 0 0 0 0 1 0 1 0 0 1 0 | 0 2 0 1 0
..... ..... .x...3.o...3.o... & ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 0 0 4 0 0 0 0 0 0 | * * * * * * * 60 * * * * * * * | 0 0 0 0 0 1 1 0 0 0 1 | 0 1 1 1 0
.xo..3.ox.. ..... ..... .....&#x & ♦ 0 3 3 | 0 0 3 0 6 3 | 0 0 0 0 0 1 0 0 3 3 0 0 1 0 | * * * * * * * * 120 * * * * * * | 0 0 1 0 0 0 0 2 0 0 0 | 0 2 0 0 1
.xo.. ..... ..... .ox.. .....&#x & ♦ 0 2 2 | 0 0 1 0 4 1 | 0 0 0 0 0 0 0 0 2 0 0 2 0 0 | * * * * * * * * * 360 * * * * * | 0 0 0 1 0 0 0 1 1 0 0 | 0 1 1 0 1
..... .ox..3.xo.. ..... .....&#x & ♦ 0 3 3 | 0 0 0 3 6 3 | 0 0 0 0 0 0 1 0 0 3 3 0 0 1 | * * * * * * * * * * 120 * * * * | 0 0 1 0 0 0 0 0 0 2 0 | 0 3 0 0 0
..... .oxo. ..... .oxo. .....&#xt ♦ 0 2 4 | 0 0 0 0 8 4 | 0 0 0 0 0 0 0 0 0 4 0 4 0 0 | * * * * * * * * * * * 180 * * * | 0 0 0 0 0 0 0 2 0 1 0 | 0 2 0 0 1
..... ..... .xo..3.ox.. .....&#x & ♦ 0 3 3 | 0 0 0 3 6 3 | 0 0 0 0 0 0 0 1 0 0 3 3 0 1 | * * * * * * * * * * * * 240 * * | 0 0 0 1 0 0 0 0 0 1 1 | 0 2 1 0 0
..... ..... ..... .ox..3.oo..&#x & ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 0 3 1 0 | * * * * * * * * * * * * * 240 * | 0 0 0 0 0 0 0 1 1 0 1 | 0 1 1 0 1
..o..3..x..3..o.. ..... ..... & ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * * * * 30 | 0 0 1 0 0 0 0 0 0 0 2 | 0 2 1 0 0
------------------------------------+-----------+-------------------------+-------------------------------------------------------+-------------------------------------------------------+-------------------------------------+--------------
o....3x....3o....3o.... ..... & ♦ 10 0 0 | 30 0 0 0 0 0 | 10 20 0 0 0 0 0 0 0 0 0 0 0 0 | 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 | 12 * * * * * * * * * * | 1 1 0 0 0
..... x....3o....3o....3o.... & ♦ 5 0 0 | 10 0 0 0 0 0 | 0 10 0 0 0 0 0 0 0 0 0 0 0 0 | 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 12 * * * * * * * * * | 1 0 0 1 0
oxo..3xox..3oxo.. ..... .....&#xt & ♦ 6 12 6 | 12 24 12 12 24 12 | 4 4 12 12 12 4 4 0 12 12 12 0 4 4 | 1 0 4 6 4 0 0 0 4 0 4 0 0 0 1 | * * 30 * * * * * * * * | 0 2 0 0 0
oxo.. ..... oxo..3oox.. .....&#xt & ♦ 1 6 3 | 0 6 3 6 12 3 | 0 0 3 0 6 0 0 2 6 0 6 6 0 1 | 0 0 0 3 0 2 0 0 0 3 0 0 2 0 0 | * * * 120 * * * * * * * | 0 1 1 0 0
..... xo...3ox...3oo... .....&#x & ♦ 4 6 0 | 6 12 0 12 0 0 | 0 4 0 6 12 0 4 4 0 0 0 0 0 0 | 0 1 0 0 4 4 1 0 0 0 0 0 0 0 0 | * * * * 60 * * * * * * | 0 1 0 1 0
..... ..... ox...3oo...3oo...&#x & ♦ 1 4 0 | 0 4 0 6 0 0 | 0 0 0 0 6 0 0 4 0 0 0 0 0 0 | 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 | * * * * * 60 * * * * * | 0 0 1 1 0
..... .o...3.x...3.o...3.o... & ♦ 0 10 0 | 0 0 0 30 0 0 | 0 0 0 0 0 0 10 20 0 0 0 0 0 0 | 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 | * * * * * * 12 * * * * | 0 1 0 1 0
.xoo.3.oxo. ..... .oxo. .....&#xt & ♦ 0 4 6 | 0 0 3 0 18 9 | 0 0 0 0 0 1 0 0 6 9 0 12 2 0 | 0 0 0 0 0 0 0 0 2 3 0 3 0 2 0 | * * * * * * * 120 * * * | 0 1 0 0 1
.xo.. ..... ..... .ox..3.oo..&#x & ♦ 0 2 3 | 0 0 1 0 6 3 | 0 0 0 0 0 0 0 0 3 0 0 6 1 0 | 0 0 0 0 0 0 0 0 0 3 0 0 0 2 0 | * * * * * * * * 120 * * | 0 0 1 0 1
..... .oxo.3.xox.3.oxo. .....&#xt & ♦ 0 12 12 | 0 0 0 24 48 24 | 0 0 0 0 0 0 8 8 0 24 24 24 0 8 | 0 0 0 0 0 0 2 0 0 0 8 6 8 0 0 | * * * * * * * * * 30 * | 0 2 0 0 0
..... ..... .xo..3.ox..3.oo..&#x & ♦ 0 4 6 | 0 0 0 6 12 12 | 0 0 0 0 0 0 0 4 0 0 6 12 4 4 | 0 0 0 0 0 0 0 1 0 0 0 0 4 4 1 | * * * * * * * * * * 60 | 0 1 1 0 0
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o....3x....3o....3o....3o.... & ♦ 15 0 0 | 60 0 0 0 0 0 | 20 60 0 0 0 0 0 0 0 0 0 0 0 0 | 15 30 0 0 0 0 0 0 0 0 0 0 0 0 0 | 6 6 0 0 0 0 0 0 0 0 0 | 2 * * * *
oxoo.3xoxo.3oxox.3ooxo. .....&#xt & ♦ 10 40 30 | 30 60 30 90 180 90 | 10 20 30 30 60 10 30 40 60 90 90 120 20 30 | 5 5 10 30 20 20 10 5 20 30 30 30 40 20 5 | 1 0 5 10 5 0 1 10 0 5 5 | * 12 * * *
oxo.. ..... oxo..3oox..3ooo..&#xt & ♦ 1 8 6 | 0 8 4 12 24 12 | 0 0 4 0 12 0 0 8 12 0 12 24 4 4 | 0 0 0 6 0 8 0 2 0 12 0 0 8 8 1 | 0 0 0 4 0 2 0 0 4 0 2 | * * 30 * *
..... xo...3ox...3oo...3oo...&#x & ♦ 5 10 0 | 10 20 0 30 0 0 | 0 10 0 10 30 0 10 20 0 0 0 0 0 0 | 0 5 0 0 10 20 5 5 0 0 0 0 0 0 0 | 0 1 0 0 5 5 1 0 0 0 0 | * * * 12 *
.xoo.3.oxo. ..... .oxo.3.oox.&#xt ♦ 0 6 9 | 0 0 6 0 36 18 | 0 0 0 0 0 2 0 0 18 18 0 36 6 0 | 0 0 0 0 0 0 0 0 6 18 0 9 0 12 0 | 0 0 0 0 0 0 0 6 6 0 0 | * * * * 20
oooxxo4oqqooq oooxox4qoqoqo ooooxx4qqoqoo&#zx → height = 0
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