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Acronym
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ek
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Name
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diacosipentacontahexazetton,
octacross (β8),
aeroyott(id),
octaexal antiprism,
vertex figure of vee,
(one of the) Delone cell(s) of lattice E8,
Gosset polytope 51,1,
lattice C8 contact polytope (span of its small roots),
equatorial cross-section of vertex-first vee
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Circumradius
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1/sqrt(2) = 0.707107
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Inradius
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1/4 = 0.25
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Lace city
in approx. ASCII-art
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 ©
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o -- o3o3o3o3o3o4o (point)
o g o -- x3o3o3o3o3o4o (zee)
o -- o3o3o3o3o3o4o (point)
where:
o = o3o3o3o3o4o (point)
g = x3o3o3o3o4o (gee)
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|
©
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a -- x o3o3o3o4o (line)
b H b -- o x3o3o3o4o (perp gee)
a -- x o3o3o3o4o (line)
where:
a = x o o3o3o4o (line)
b = o x o3o3o4o (perp line)
H = o o x3o3o4o (perp hex)
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o3o3o3o3o3o x3o3o3o3o3o
o3o3o3o3o3x o3o3o3o3o3o
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x o3o3o3o3o o x3o3o3o3o
o o3o3o3o3x x o3o3o3o3o
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x3o o3o3o3o o3o x3o3o3o
o3o o3o3o3x o3x o3o3o3o
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x3o3o o3o3o o3o3o x3o3o
o3o3o o3o3x o3o3x o3o3o
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Coordinates
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(1/sqrt(2), 0, 0, 0, 0, 0, 0, 0) & all permutations, all changes of sign
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Volume
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1/2520 = 0.00039683
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Surface
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4/315 = 0.012698
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Rel. Roundness
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105 π4/65536 = 15.606620 %
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Dual
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octo
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Dihedral angles
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- at hop between oca and oca: arccos(-3/4) = 138.590378°
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Face vector
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16, 112, 448, 1120, 1792, 1792, 1024, 256
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Confer
|
- more general:
-
xPo3o...o3o4o
- related segmentozetta:
-
zeepy
geeasc
hexepe
- general polytopal classes:
-
Wythoffian polyzetta
orthoplex
noble polytopes
segmentozetta
fundamental lace prisms
Coxeter-Elte-Gosset polytopes
- analogs:
-
regular orthoplex On
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External
links
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Incidence matrix according to Dynkin symbol
x3o3o3o3o3o3o4o
. . . . . . . . | 16 ♦ 14 | 84 | 280 | 560 | 672 | 448 | 128
----------------+----+-----+-----+------+------+------+------+----
x . . . . . . . | 2 | 112 ♦ 12 | 60 | 160 | 240 | 192 | 64
----------------+----+-----+-----+------+------+------+------+----
x3o . . . . . . | 3 | 3 | 448 ♦ 10 | 40 | 80 | 80 | 32
----------------+----+-----+-----+------+------+------+------+----
x3o3o . . . . . ♦ 4 | 6 | 4 | 1120 ♦ 8 | 24 | 32 | 16
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o . . . . ♦ 5 | 10 | 10 | 5 | 1792 ♦ 6 | 12 | 8
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o . . . ♦ 6 | 15 | 20 | 15 | 6 | 1792 | 4 | 4
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o3o . . ♦ 7 | 21 | 35 | 35 | 21 | 7 | 1024 | 2
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o3o3o . ♦ 8 | 28 | 56 | 70 | 56 | 28 | 8 | 256
x3o3o3o3o3o3o4/3o
. . . . . . . . | 16 ♦ 14 | 84 | 280 | 560 | 672 | 448 | 128
------------------+----+-----+-----+------+------+------+------+----
x . . . . . . . | 2 | 112 ♦ 12 | 60 | 160 | 240 | 192 | 64
------------------+----+-----+-----+------+------+------+------+----
x3o . . . . . . | 3 | 3 | 448 ♦ 10 | 40 | 80 | 80 | 32
------------------+----+-----+-----+------+------+------+------+----
x3o3o . . . . . ♦ 4 | 6 | 4 | 1120 ♦ 8 | 24 | 32 | 16
------------------+----+-----+-----+------+------+------+------+----
x3o3o3o . . . . ♦ 5 | 10 | 10 | 5 | 1792 ♦ 6 | 12 | 8
------------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o . . . ♦ 6 | 15 | 20 | 15 | 6 | 1792 | 4 | 4
------------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o3o . . ♦ 7 | 21 | 35 | 35 | 21 | 7 | 1024 | 2
------------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o3o3o . ♦ 8 | 28 | 56 | 70 | 56 | 28 | 8 | 256
o3o3o *b3o3o3o3o3x
. . . . . . . . | 16 ♦ 14 | 84 | 280 | 560 | 672 | 448 | 64 64
-------------------+----+-----+-----+------+------+------+------+--------
. . . . . . . x | 2 | 112 ♦ 12 | 60 | 160 | 240 | 192 | 32 32
-------------------+----+-----+-----+------+------+------+------+--------
. . . . . . o3x | 3 | 3 | 448 ♦ 10 | 40 | 80 | 80 | 16 16
-------------------+----+-----+-----+------+------+------+------+--------
. . . . . o3o3x ♦ 4 | 6 | 4 | 1120 ♦ 8 | 24 | 32 | 8 8
-------------------+----+-----+-----+------+------+------+------+--------
. . . . o3o3o3x ♦ 5 | 10 | 10 | 5 | 1792 ♦ 6 | 12 | 4 4
-------------------+----+-----+-----+------+------+------+------+--------
. . . o3o3o3o3x ♦ 6 | 15 | 20 | 15 | 6 | 1792 | 4 | 2 2
-------------------+----+-----+-----+------+------+------+------+--------
. o . *b3o3o3o3o3x ♦ 7 | 21 | 35 | 35 | 21 | 7 | 1024 | 1 1
-------------------+----+-----+-----+------+------+------+------+--------
o3o . *b3o3o3o3o3x ♦ 8 | 28 | 56 | 70 | 56 | 28 | 7 | 128 *
. o3o *b3o3o3o3o3x ♦ 8 | 28 | 56 | 70 | 56 | 28 | 7 | * 128
xo3oo3oo3oo3oo3oo3ox&#x → height = 1/2
(oca || dual oca)
o.3o.3o.3o.3o.3o.3o. & | 16 ♦ 7 7 | 21 63 | 35 140 105 | 35 175 350 | 21 126 315 210 | 7 49 147 245 | 1 8 28 56 35
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x. .. .. .. .. .. .. & | 2 | 56 * ♦ 6 6 | 15 30 15 | 20 60 80 | 15 60 105 60 | 6 30 66 90 | 1 6 16 26 15
oo3oo3oo3oo3oo3oo3oo&#x | 2 | * 56 ♦ 0 12 | 0 30 30 | 0 40 120 | 0 30 120 90 | 0 12 60 120 | 0 2 12 30 20
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o. .. .. .. .. .. & | 3 | 3 0 | 112 * ♦ 5 5 0 | 10 20 10 | 10 30 30 10 | 5 20 30 25 | 1 5 10 11 5
xo .. .. .. .. .. ..&#x & | 3 | 1 2 | * 336 ♦ 0 5 5 | 0 10 30 | 0 10 40 30 | 0 5 25 50 | 0 1 6 15 10
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | 140 * * ♦ 4 4 0 | 6 12 6 0 | 4 12 12 4 | 1 4 6 4 1
xo3oo .. .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * 560 * ♦ 0 4 4 | 0 6 12 6 | 0 4 12 16 | 0 1 4 7 4
xo .. .. .. .. .. ox&#x ♦ 4 | 2 4 | 0 4 | * * 420 ♦ 0 0 8 | 0 0 12 12 | 0 0 8 24 | 0 0 2 8 6
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o.3o. .. .. .. & ♦ 5 | 10 0 | 10 0 | 5 0 0 | 112 * * ♦ 3 3 0 0 | 3 6 3 0 | 1 3 3 1 0
xo3oo3oo .. .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 1 4 0 | * 560 * ♦ 0 3 3 0 | 0 3 6 3 | 0 1 3 3 1
xo3oo .. .. .. .. ox&#x & ♦ 5 | 4 6 | 1 9 | 0 2 3 | * * 1120 ♦ 0 0 3 3 | 0 0 3 9 | 0 0 1 4 3
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o.3o.3o. .. .. & ♦ 6 | 15 0 | 20 0 | 15 0 0 | 6 0 0 | 56 * * * | 2 2 0 0 | 1 2 1 0 0
xo3oo3oo3oo .. .. ..&#x & ♦ 6 | 10 5 | 10 10 | 5 10 0 | 1 5 0 | * 336 * * | 0 2 2 0 | 0 1 2 1 0
xo3oo3oo .. .. .. ox&#x & ♦ 6 | 7 8 | 4 16 | 1 8 6 | 0 2 4 | * * 840 * | 0 0 2 2 | 0 0 1 2 1
xo3oo .. .. .. oo3ox&#x ♦ 6 | 6 9 | 2 18 | 0 6 9 | 0 0 6 | * * * 560 | 0 0 0 4 | 0 0 0 2 2
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o.3o.3o.3o. .. & ♦ 7 | 21 0 | 35 0 | 35 0 0 | 21 0 0 | 7 0 0 0 | 16 * * * | 1 1 0 0 0
xo3oo3oo3oo3oo .. ..&#x & ♦ 7 | 15 6 | 20 15 | 15 20 0 | 6 15 0 | 1 6 0 0 | * 112 * * | 0 1 1 0 0
xo3oo3oo3oo .. .. ox&#x & ♦ 7 | 11 10 | 10 25 | 5 20 10 | 1 10 10 | 0 2 5 0 | * * 336 * | 0 0 1 1 0
xo3oo3oo .. .. oo3ox&#x & ♦ 7 | 9 12 | 5 30 | 1 16 18 | 0 3 18 | 0 0 3 4 | * * * 560 | 0 0 0 1 1
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o.3o.3o.3o.3o. & ♦ 8 | 28 0 | 56 0 | 70 0 0 | 56 0 0 | 28 0 0 0 | 8 0 0 0 | 2 * * * *
xo3oo3oo3oo3oo3oo ..&#x & ♦ 8 | 21 7 | 35 21 | 35 35 0 | 21 35 0 | 7 21 0 0 | 1 7 0 0 | * 16 * * *
xo3oo3oo3oo3oo .. ox&#x & ♦ 8 | 16 12 | 20 36 | 15 40 15 | 6 30 20 | 1 12 15 0 | 0 2 6 0 | * * 56 * *
xo3oo3oo3oo .. oo3ox&#x & ♦ 8 | 13 15 | 11 45 | 5 35 30 | 1 15 40 | 0 3 15 10 | 0 0 3 5 | * * * 112 *
xo3oo3oo .. oo3oo3ox&#x ♦ 8 | 12 16 | 8 48 | 2 32 36 | 0 8 48 | 0 0 12 16 | 0 0 0 8 | * * * * 70
oqo xoo3ooo3ooo3ooo3ooo3oox&#xt → both heights = 1/sqrt(14) = 0.267261
(hop || perp pseudo q-line || dual hop)
...
xo3oo3oo4oo ox3oo3oo4oo&#zx → height = 0
(tegum product of 2 hex)
o.3o.3o.4o. o.3o.3o.4o. & | 16 ♦ 6 8 | 12 72 | 8 128 144 | 80 480 | 288 384 | 448 | 128
------------------------------+----+-------+--------+------------+----------+----------+------+----
x. .. .. .. .. .. .. .. & | 2 | 48 * ♦ 4 8 | 4 32 24 | 32 128 | 112 128 | 192 | 64
oo3oo3oo4oo oo3oo3oo4oo&#x | 2 | * 64 ♦ 0 12 | 0 24 36 | 16 144 | 96 144 | 192 | 64
------------------------------+----+-------+--------+------------+----------+----------+------+----
x.3o. .. .. .. .. .. .. & | 3 | 3 0 | 64 * ♦ 2 8 0 | 16 24 | 48 32 | 80 | 32
xo .. .. .. .. .. .. ..&#x & | 3 | 1 2 | * 384 ♦ 0 4 6 | 4 36 | 32 48 | 80 | 32
------------------------------+----+-------+--------+------------+----------+----------+------+----
x.3o.3o. .. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | 32 * * ♦ 8 0 | 24 0 | 32 | 16
xo3oo .. .. .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * 512 * ♦ 2 6 | 12 12 | 32 | 16
xo .. .. .. ox .. .. ..&#x ♦ 4 | 2 4 | 0 4 | * * 576 ♦ 0 8 | 8 16 | 32 | 16
------------------------------+----+-------+--------+------------+----------+----------+------+----
xo3oo3oo .. .. .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 1 4 0 | 256 * ♦ 6 0 | 12 | 8
xo3oo .. .. ox .. .. ..&#x & ♦ 5 | 4 6 | 1 9 | 0 2 3 | * 1536 ♦ 2 4 | 12 | 8
------------------------------+----+-------+--------+------------+----------+----------+------+----
xo3oo3oo .. ox .. .. ..&#x & ♦ 6 | 7 8 | 4 16 | 1 8 6 | 2 4 | 768 * | 4 | 4
xo3oo .. .. ox3oo .. ..&#x ♦ 6 | 6 9 | 2 18 | 0 6 9 | 0 6 | * 1024 | 4 | 4
------------------------------+----+-------+--------+------------+----------+----------+------+----
xo3oo3oo .. ox3oo .. ..&#x & ♦ 7 | 9 12 | 5 30 | 1 16 18 | 3 18 | 3 4 | 1024 | 2
------------------------------+----+-------+--------+------------+----------+----------+------+----
xo3oo3oo .. ox3oo3oo ..&#x ♦ 8 | 12 16 | 8 48 | 2 32 36 | 8 48 | 12 16 | 8 | 256
xo3oo3oo *b3oo ox3oo3oo *f3oo&#zx → height = 0
(tegum product of 2 hex)
o.3o.3o. *b3o. o.3o.3o. *f3o. & | 16 ♦ 6 8 | 12 72 | 4 4 128 144 | 40 40 480 | 144 144 384 | 224 224 | 32 64 32
------------------------------------+----+-------+--------+---------------+--------------+--------------+---------+----------
x. .. .. .. .. .. .. .. & | 2 | 48 * ♦ 4 8 | 2 2 32 24 | 16 16 128 | 56 56 128 | 96 96 | 16 32 16
oo3oo3oo *b3oo oo3oo3oo *f3oo&#x | 2 | * 64 ♦ 0 12 | 0 0 24 36 | 8 8 144 | 48 48 144 | 96 96 | 16 32 16
------------------------------------+----+-------+--------+---------------+--------------+--------------+---------+----------
x.3o. .. .. .. .. .. .. & | 3 | 3 0 | 64 * ♦ 1 1 8 0 | 8 8 24 | 24 24 32 | 40 40 | 8 16 8
xo .. .. .. .. .. .. ..&#x & | 3 | 1 2 | * 384 ♦ 0 0 4 6 | 2 2 36 | 16 16 48 | 40 40 | 8 16 8
------------------------------------+----+-------+--------+---------------+--------------+--------------+---------+----------
x.3o.3o. .. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | 16 * * * ♦ 8 0 0 | 24 0 0 | 32 0 | 8 8 0
x.3o. .. *b3o. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | * 16 * * ♦ 0 8 0 | 0 24 0 | 0 32 | 0 8 8
xo3oo .. .. .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * * 512 * ♦ 1 1 6 | 6 6 12 | 16 16 | 4 8 4
xo .. .. .. ox .. .. ..&#x ♦ 4 | 2 4 | 0 4 | * * * 576 ♦ 0 0 8 | 4 4 16 | 16 16 | 4 8 4
------------------------------------+----+-------+--------+---------------+--------------+--------------+---------+----------
xo3oo3oo .. .. .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 1 0 4 0 | 128 * * ♦ 6 0 0 | 12 0 | 4 4 0
xo3oo .. *b3oo .. .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 0 1 4 0 | * 128 * ♦ 0 6 0 | 0 12 | 0 4 4
xo3oo .. .. ox .. .. ..&#x & ♦ 5 | 4 6 | 1 9 | 0 0 2 3 | * * 1536 ♦ 1 1 4 | 6 6 | 2 4 2
------------------------------------+----+-------+--------+---------------+--------------+--------------+---------+----------
xo3oo3oo .. ox .. .. ..&#x & ♦ 6 | 7 8 | 4 16 | 1 0 8 6 | 2 0 4 | 384 * * | 4 0 | 2 2 0
xo3oo .. *b3oo ox .. .. ..&#x & ♦ 6 | 7 8 | 4 16 | 0 1 8 6 | 0 2 4 | * 384 * | 0 4 | 0 2 2
xo3oo .. .. ox3oo .. ..&#x ♦ 6 | 6 9 | 2 18 | 0 0 6 9 | 0 0 6 | * * 1024 | 2 2 | 1 2 1
------------------------------------+----+-------+--------+---------------+--------------+--------------+---------+----------
xo3oo3oo .. ox3oo .. ..&#x & ♦ 7 | 9 12 | 5 30 | 1 0 16 18 | 3 0 18 | 3 0 4 | 512 * | 1 1 0
xo3oo .. *b3oo ox3oo .. ..&#x & ♦ 7 | 9 12 | 5 30 | 0 1 16 18 | 0 3 18 | 0 3 4 | * 512 | 0 1 1
------------------------------------+----+-------+--------+---------------+--------------+--------------+---------+----------
xo3oo3oo .. ox3oo3oo ..&#x ♦ 8 | 12 16 | 8 48 | 2 0 32 36 | 8 0 48 | 12 0 16 | 8 0 | 64 * *
xo3oo3oo .. ox3oo .. *f3oo&#x & ♦ 8 | 12 16 | 8 48 | 1 1 32 36 | 4 4 48 | 6 6 16 | 4 4 | * 128 *
xo3oo .. *b3oo ox3oo .. *f3oo&#x ♦ 8 | 12 16 | 8 48 | 0 2 32 36 | 0 8 48 | 0 12 16 | 0 8 | * * 64
xo3oo3oo4oo ox3oo3oo *f3oo&#zx → height = 0
(tegum product of 2 hex)
o.3o.3o.4o. o.3o.3o. *f3o. | 8 * ♦ 6 8 0 | 12 48 24 0 | 8 96 144 32 0 0 | 64 288 192 8 8 | 192 384 48 48 | 256 96 96 | 64 64
.o3.o3.o4.o .o3.o3.o *f3.o | * 8 ♦ 0 8 6 | 0 24 48 12 | 0 32 144 96 4 4 | 16 192 288 32 32 | 96 384 96 96 | 192 128 128 | 64 64
------------------------------+-----+----------+---------------+--------------------+-------------------+------------------+-------------+--------
x. .. .. .. .. .. .. .. | 2 0 | 24 * * ♦ 4 8 0 0 | 4 32 24 0 0 0 | 32 96 32 0 0 | 96 128 8 8 | 128 32 32 | 32 32
oo3oo3oo4oo oo3oo3oo *f3oo&#x | 1 1 | * 64 * ♦ 0 6 6 0 | 0 12 36 12 0 0 | 8 72 72 4 4 | 72 144 36 36 | 96 48 48 | 32 32
.. .. .. .. .x .. .. .. | 0 2 | * * 24 ♦ 0 0 8 4 | 0 0 24 32 2 2 | 0 32 96 16 16 | 16 128 48 48 | 64 64 64 | 32 32
------------------------------+-----+----------+---------------+--------------------+-------------------+------------------+-------------+--------
x.3o. .. .. .. .. .. .. | 3 0 | 3 0 0 | 32 * * * ♦ 2 8 0 0 0 0 | 16 24 0 0 0 | 48 32 0 0 | 64 8 8 | 16 16
xo .. .. .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 192 * * ♦ 0 4 6 0 0 0 | 4 24 12 0 0 | 24 48 4 4 | 48 16 16 | 16 16
.. .. .. .. ox .. .. ..&#x | 1 2 | 0 2 1 | * * 192 * ♦ 0 0 6 4 0 0 | 0 12 24 2 2 | 8 48 12 12 | 32 24 24 | 16 16
.. .. .. .. .x3.o .. .. | 0 3 | 0 0 3 | * * * 32 ♦ 0 0 0 8 1 1 | 0 0 24 8 8 | 0 32 24 24 | 16 32 32 | 16 16
------------------------------+-----+----------+---------------+--------------------+-------------------+------------------+-------------+--------
x.3o.3o. .. .. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 16 * * * * * ♦ 8 0 0 0 0 | 24 0 0 0 | 32 0 0 | 8 8
xo3oo .. .. .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * 256 * * * * ♦ 2 6 0 0 0 | 12 12 0 0 | 24 4 4 | 8 8
xo .. .. .. ox .. .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * 576 * * * ♦ 0 4 4 0 0 | 4 16 2 2 | 16 8 8 | 8 8
.. .. .. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * 256 * * ♦ 0 0 6 1 1 | 0 12 6 6 | 8 12 12 | 8 8
.. .. .. .. .x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * 8 * ♦ 0 0 0 8 0 | 0 0 24 0 | 0 32 0 | 16 0
.. .. .. .. .x3.o .. *f3.o ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * * 8 ♦ 0 0 0 0 8 | 0 0 0 24 | 0 0 32 | 0 16
------------------------------+-----+----------+---------------+--------------------+-------------------+------------------+-------------+--------
xo3oo3oo .. .. .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 1 4 0 0 0 0 | 128 * * * * ♦ 6 0 0 0 | 12 0 0 | 4 4
xo3oo .. .. ox .. .. ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 0 2 3 0 0 0 | * 768 * * * ♦ 2 4 0 0 | 8 2 2 | 4 4
xo .. .. .. ox3oo .. ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 0 3 2 0 0 | * * 768 * * ♦ 0 4 1 1 | 4 4 4 | 4 4
.. .. .. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 4 1 0 | * * * 64 * ♦ 0 0 6 0 | 0 12 0 | 8 0
.. .. .. .. ox3oo .. *f3oo&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 4 0 1 | * * * * 64 ♦ 0 0 0 6 | 0 0 12 | 0 8
------------------------------+-----+----------+---------------+--------------------+-------------------+------------------+-------------+--------
xo3oo3oo .. ox .. .. ..&#x ♦ 4 2 | 6 8 1 | 4 12 4 0 | 1 8 6 0 0 0 | 2 4 0 0 0 | 384 * * * | 4 0 0 | 2 2
xo3oo .. .. ox3oo .. ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 | 0 3 9 3 0 0 | 0 3 3 0 0 | * 1024 * * | 2 1 1 | 2 2
xo .. .. .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 0 6 8 1 0 | 0 0 4 2 0 | * * 192 * | 0 4 0 | 4 0
xo .. .. .. ox3oo .. *f3oo&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 0 6 8 0 1 | 0 0 4 0 2 | * * * 192 | 0 0 4 | 0 4
------------------------------+-----+----------+---------------+--------------------+-------------------+------------------+-------------+--------
xo3oo3oo .. ox3oo .. ..&#x ♦ 4 3 | 6 12 3 | 4 18 12 1 | 1 12 18 4 0 0 | 3 12 6 0 0 | 3 4 0 0 | 512 * * | 1 1
xo3oo .. .. ox3oo3oo ..&#x ♦ 3 4 | 3 12 6 | 1 12 18 4 | 0 4 18 12 1 0 | 0 6 12 3 0 | 0 4 3 0 | * 256 * | 2 0
xo3oo .. .. ox3oo .. *f3oo&#x ♦ 3 4 | 3 12 6 | 1 12 18 4 | 0 4 18 12 0 1 | 0 6 12 0 3 | 0 4 0 3 | * * 256 | 0 2
------------------------------+-----+----------+---------------+--------------------+-------------------+------------------+-------------+--------
xo3oo3oo .. ox3oo3oo ..&#x ♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 1 0 | 4 24 24 4 0 | 6 16 6 0 | 4 4 0 | 128 *
xo3oo3oo .. ox3oo .. *f3oo&#x ♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 0 1 | 4 24 24 0 4 | 6 16 0 6 | 4 0 4 | * 128
xooo4oooo oxoo4oooo ooxo4oooo ooox4oooo&#zx → all pw. heights = 0
(tegum product of 4 {4})
o...4o... o...4o... o...4o... o...4o... & | 16 ♦ 2 12 | 36 48 | 24 192 64 | 240 320 | 96 576 | 448 | 128
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
x... .... .... .... .... .... .... .... & | 2 | 16 * ♦ 12 0 | 12 48 0 | 96 64 | 48 192 | 192 | 64
oo..4oo.. oo..4oo.. oo..4oo.. oo..4oo..&#x & | 2 | * 96 ♦ 4 8 | 4 40 16 | 64 96 | 32 208 | 192 | 64
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
xo.. .... .... .... .... .... .... ....&#x & | 3 | 1 2 | 192 * ♦ 2 8 0 | 24 16 | 16 64 | 80 | 32
ooo.4ooo. ooo.4ooo. ooo.4ooo. ooo.4ooo.&#x & | 3 | 0 3 | * 256 ♦ 0 6 4 | 12 28 | 8 72 | 80 | 32
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
xo.. .... ox.. .... .... .... .... ....&#x & ♦ 4 | 2 4 | 4 0 | 96 * * ♦ 8 0 | 8 16 | 32 | 16
xoo. .... .... .... .... .... .... ....&#x & ♦ 4 | 1 5 | 2 2 | * 768 * ♦ 4 4 | 4 20 | 32 | 16
oooo4oooo oooo4oooo oooo4oooo oooo4oooo&#x ♦ 4 | 0 6 | 0 4 | * * 256 ♦ 0 8 | 0 24 | 32 | 16
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
xoo. .... oxo. .... .... .... .... ....&#x & ♦ 5 | 2 8 | 6 4 | 1 4 0 | 768 * ♦ 2 4 | 12 | 8
xooo .... .... .... .... .... .... ....&#x & ♦ 5 | 1 9 | 3 7 | 0 3 2 | * 1024 ♦ 0 6 | 12 | 8
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
xoo. .... oxo. .... oox. .... .... ....&#x & ♦ 6 | 3 12 | 12 8 | 3 12 0 | 6 0 | 256 * | 4 | 4
xooo .... oxoo .... .... .... .... ....&#x & ♦ 6 | 2 13 | 8 12 | 1 10 4 | 2 4 | * 1536 | 4 | 4
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
xooo .... oxoo .... ooxo .... .... ....&#x & ♦ 7 | 3 18 | 15 20 | 3 24 8 | 9 12 | 1 6 | 1024 | 2
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
xooo .... oxoo .... ooxo .... ooox ....&#x & ♦ 8 | 4 24 | 24 32 | 6 48 16 | 24 32 | 4 24 | 8 | 256
xooo xooo oxoo oxoo ooxo ooxo ooox ooox&#zx → all pw. heights = 0
(tegum product of 4 {4})
o... o... o... o... o... o... o... o... & | 16 ♦ 2 12 | 36 48 | 24 192 64 | 240 320 | 96 576 | 448 | 128
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
x... .... .... .... .... .... .... .... & | 2 | 16 * ♦ 12 0 | 12 48 0 | 96 64 | 48 192 | 192 | 64
oo.. oo.. oo.. oo.. oo.. oo.. oo.. oo..&#x & | 2 | * 96 ♦ 4 8 | 4 40 16 | 64 96 | 32 208 | 192 | 64
----------------------------------------------+----+-------+---------+------------+----------+----------+------+----
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