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Acronym
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hocto (alt.: gecdify)
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Name
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hemiocteract,
64(=g)+48(=c)-diminished fy,
Gosset polytope 15,1
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Circumradius
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1
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Inradius
wrt. oca
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3/4 = 0.75
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Inradius
wrt. hesa
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1/sqrt(8) = 0.353553
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Lace city
in approx. ASCII-art
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 ©
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H h where:
H = x3o3o *b3o3o3o (hax)
h H h = o3o3x *b3o3o3o (alt. hax)
| |
| +- o3o3x *b3o3o3o3o (hesa)
+----- x3o3o *b3o3o3o3o (alt. hesa)
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_+----------------- x3o3o3o3o3o3o (oca)
_- _+------------ o3o3x3o3o3o3o (broc)
_- _- _+------- o3o3o3o3x3o3o (inv. broc)
_- _- _- _+-- o3o3o3o3o3o3x (dual oca)
_- _- _- _-
o -- o3o3o3o3o3o3o (point)
h r -- o3x3o3o3o3o3o (roc)
b B -- o3o3o3x3o3o3o (he)
R H -- o3o3o3o3o3x3o (inv. roc)
o -- o3o3o3o3o3o3o (point)
\ \
\ +-- x3o3o *b3o3o3o3o (hesa)
+--------- o3o3x *b3o3o3o3o (alt. hesa)
where:
o = o3o3o3o3o3o (point)
h = x3o3o3o3o3o (hop)
H = o3o3o3o3o3x (dual hop)
r = o3x3o3o3o3o (ril)
R = o3o3o3o3x3o (inv. ril)
b = o3o3x3o3o3o (bril)
B = o3o3o3x3o3o (inv. bril)
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Coordinates
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(1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8)) & all permutations, all even changes of sign
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Volume
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157/2520 = 0.062302
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Surface
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[2+311 sqrt(2)]/315 = 1.402605
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Dihedral angles
(at margins)
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Face vector
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128, 1792, 7168, 10752, 8288, 4032, 1136, 144
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Confer
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- uniform relative:
-
fy
hexdip
- related segmentozetta:
-
rocpy
broca
- related scaliforms:
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codify
- general polytopal classes:
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Wythoffian polyzetta
segmentozetta
fundamental lace prisms
Coxeter-Elte-Gosset polytopes
- analogs:
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demihypercube Dn
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External
links
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This polyzetton is a hemiation of octo, just as hextes.
But this hemiation here is only wrt. all 8 coordinates, while that of hextes is wrt. the first 4 coordinates only.
–
None the same this alternation for hextes, when directly being applied to octo,
would produce different edge sizes, a fact that still can be overcome by resizements.
Therefore that relation between hextes and octo
is just a combinatorical one, not a metrical one.
In contrast to that the case within this polyzetton is different. All edges would come out in the same size directly.
In fact, the edges of hocto would just be the diagonals of the squares of octo.
Furthermore it can be derived as the tegum sum of 2 mutually bigyrated hexdips,
or, what comes out to be the same, as a (64+48)-diminished fy. (The latter is because fy
can be both considered as a tegum sum of hocto and rek, as well as a
tegum sum of 2 perpendicular icoes and 3 mutually gyrated hexdips
in a further subdivision of the former subsymmetry.)
Incidence matrix according to Dynkin symbol
x3o3o *b3o3o3o3o3o
. . . . . . . . | 128 ♦ 28 | 168 | 56 280 | 70 280 | 56 168 | 28 56 | 8 8
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x . . . . . . . | 2 | 1792 ♦ 12 | 6 30 | 15 40 | 20 30 | 15 12 | 6 2
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o . . . . . . | 3 | 3 | 7168 | 1 5 | 5 10 | 10 10 | 10 5 | 5 1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o . . . . . ♦ 4 | 6 | 4 | 1792 * ♦ 5 0 | 10 0 | 10 0 | 5 0
x3o . *b3o . . . . ♦ 4 | 6 | 4 | * 8960 | 1 4 | 4 6 | 6 4 | 4 1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o . . . . ♦ 8 | 24 | 32 | 8 8 | 1120 * ♦ 4 0 | 6 0 | 4 0
x3o . *b3o3o . . . ♦ 5 | 10 | 10 | 0 5 | * 7168 | 1 3 | 3 3 | 3 1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o3o . . . ♦ 16 | 80 | 160 | 40 80 | 10 16 | 448 * | 3 0 | 3 0
x3o . *b3o3o3o . . ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 3584 | 1 2 | 2 1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o3o3o . . ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 | 112 * | 2 0
x3o . *b3o3o3o3o . ♦ 7 | 21 | 35 | 0 35 | 0 21 | 0 7 | * 1024 | 1 1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o3o3o3o . ♦ 64 | 672 | 2240 | 560 2240 | 280 1344 | 84 448 | 14 64 | 16 *
x3o . *b3o3o3o3o3o ♦ 8 | 28 | 56 | 0 70 | 0 56 | 0 28 | 0 8 | * 128
o3o3o3o3o3o3o4s
demi( . . . . . . . . ) | 128 ♦ 28 | 168 | 56 280 | 70 280 | 56 168 | 28 56 | 8 8
------------------------+-----+------+------+-----------+-----------+----------+----------+-------
. . . . . . o4s | 2 | 1792 ♦ 12 | 6 30 | 15 40 | 20 30 | 15 12 | 6 2
------------------------+-----+------+------+-----------+-----------+----------+----------+-------
sefa( . . . . . o3o4s ) | 3 | 3 | 7168 | 1 5 | 5 10 | 10 10 | 10 5 | 5 1
------------------------+-----+------+------+-----------+-----------+----------+----------+-------
. . . . . o3o4s ♦ 4 | 6 | 4 | 1792 * ♦ 5 0 | 10 0 | 10 0 | 5 0
sefa( . . . . o3o3o4s ) ♦ 4 | 6 | 4 | * 8960 | 1 4 | 4 6 | 6 4 | 4 1
------------------------+-----+------+------+-----------+-----------+----------+----------+-------
. . . . o3o3o4s ♦ 8 | 24 | 32 | 8 8 | 1120 * ♦ 4 0 | 6 0 | 4 0
sefa( . . . o3o3o3o4s ) ♦ 5 | 10 | 10 | 0 5 | * 7168 | 1 3 | 3 3 | 3 1
------------------------+-----+------+------+-----------+-----------+----------+----------+-------
. . . o3o3o3o4s ♦ 16 | 80 | 160 | 40 80 | 10 16 | 448 * | 3 0 | 3 0
sefa( . . o3o3o3o3o4s ) ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 3584 | 1 2 | 2 1
------------------------+-----+------+------+-----------+-----------+----------+----------+-------
. . o3o3o3o3o4s ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 | 112 * | 2 0
sefa( . o3o3o3o3o3o4s ) ♦ 7 | 21 | 35 | 0 35 | 0 21 | 0 7 | * 1024 | 1 1
------------------------+-----+------+------+-----------+-----------+----------+----------+-------
. o3o3o3o3o3o4s ♦ 64 | 672 | 2240 | 560 2240 | 280 1344 | 84 448 | 14 64 | 16 *
sefa( o3o3o3o3o3o3o4s ) ♦ 8 | 28 | 56 | 0 70 | 0 56 | 0 28 | 0 8 | * 128
starting figure: o3o3o3o3o3o3o4x
xo3oo3ox *b3oo3oo3oo3oo&#x → height = 1/sqrt(2) = 0.707107
(hesa || alternate hesa)
o.3o.3o. *b3o.3o.3o.3o. | 64 * ♦ 21 7 0 | 105 42 21 0 | 35 140 105 21 35 0 0 | 35 105 35 140 35 0 0 | 21 42 35 105 21 0 0 | 7 7 21 42 7 0 0 | 1 7 7 1 0
.o3.o3.o *b3.o3.o3.o3.o | * 64 ♦ 0 7 21 | 0 21 42 105 | 0 0 35 21 105 35 140 | 0 0 35 35 140 35 105 | 0 0 35 21 105 21 42 | 0 0 21 7 42 7 7 | 0 7 1 7 1
---------------------------+-------+-------------+---------------------+---------------------------------+---------------------------------+-----------------------------+------------------------+-------------
x. .. .. .. .. .. .. | 2 0 | 672 * * ♦ 10 2 0 0 | 5 20 10 1 0 0 0 | 10 20 5 20 0 0 0 | 10 10 10 20 0 0 0 | 5 2 10 10 0 0 0 | 1 5 2 0 0
oo3oo3oo *b3oo3oo3oo3oo&#x | 1 1 | * 448 * ♦ 0 6 6 0 | 0 0 15 6 15 0 0 | 0 0 15 20 20 0 0 | 0 0 20 15 15 0 0 | 0 0 15 6 6 0 0 | 0 6 1 1 0
.. .. .x .. .. .. .. | 0 2 | * * 672 ♦ 0 0 2 10 | 0 0 0 1 10 5 20 | 0 0 5 0 20 10 20 | 0 0 10 0 20 10 10 | 0 0 10 0 10 5 2 | 0 5 0 2 1
---------------------------+-------+-------------+---------------------+---------------------------------+---------------------------------+-----------------------------+------------------------+-------------
x.3o. .. .. .. .. .. | 3 0 | 3 0 0 | 2240 * * * | 1 4 1 0 0 0 0 | 4 6 1 4 0 0 0 | 6 4 4 6 0 0 0 | 4 1 6 4 0 0 0 | 1 4 1 0 0
xo .. .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 1344 * * | 0 0 5 1 0 0 0 | 0 0 5 10 0 0 0 | 0 0 10 10 0 0 0 | 0 0 10 5 0 0 0 | 0 5 1 0 0
.. .. ox .. .. .. ..&#x | 1 2 | 0 2 1 | * * 1344 * | 0 0 0 1 5 0 0 | 0 0 5 0 10 0 0 | 0 0 10 0 10 0 0 | 0 0 10 0 5 0 0 | 0 5 0 1 0
.. .o3.x .. .. .. .. | 0 3 | 0 0 3 | * * * 2240 | 0 0 0 0 1 1 4 | 0 0 1 0 4 4 6 | 0 0 4 0 6 6 4 | 0 0 6 0 4 4 1 | 0 4 0 1 1
---------------------------+-------+-------------+---------------------+---------------------------------+---------------------------------+-----------------------------+------------------------+-------------
x.3o.3o. .. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 560 * * * * * * ♦ 4 0 1 0 0 0 0 | 3 0 4 0 0 0 0 | 4 0 6 0 0 0 0 | 1 4 0 0 0
x.3o. .. *b3o. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | * 2240 * * * * * | 1 3 0 1 0 0 0 | 3 3 1 3 0 0 0 | 3 1 3 3 0 0 0 | 1 3 1 0 0
xo3oo .. .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * * 2240 * * * * | 0 0 4 1 0 0 0 | 0 0 4 6 0 0 0 | 0 0 6 4 0 0 0 | 0 4 1 0 0
xo .. ox .. .. .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * * 672 * * * ♦ 0 0 5 0 0 0 0 | 0 0 10 0 0 0 0 | 0 0 10 0 0 0 0 | 0 5 0 0 0
.. oo3ox .. .. .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * * 2240 * * | 0 0 1 0 4 0 0 | 0 0 4 0 6 0 0 | 0 0 6 0 4 0 0 | 0 4 0 1 0
.o3.o3.x .. .. .. .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * * 560 * ♦ 0 0 1 0 0 4 0 | 0 0 4 0 0 6 0 | 0 0 6 0 0 4 0 | 0 4 0 0 1
.. .o3.x *b3.o .. .. .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * * * 2240 | 0 0 0 0 1 1 3 | 0 0 1 0 3 3 3 | 0 0 3 0 3 3 1 | 0 3 0 1 1
---------------------------+-------+-------------+---------------------+---------------------------------+---------------------------------+-----------------------------+------------------------+-------------
x.3o.3o. *b3o. .. .. .. ♦ 8 0 | 24 0 0 | 32 0 0 0 | 8 8 0 0 0 0 0 | 280 * * * * * * ♦ 3 0 1 0 0 0 0 | 3 0 3 0 0 0 0 | 1 3 0 0 0
x.3o. .. *b3o.3o. .. .. ♦ 5 0 | 10 0 0 | 10 0 0 0 | 0 5 0 0 0 0 0 | * 1344 * * * * * | 1 2 0 1 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0 0
xo3oo3ox .. .. .. ..&#x ♦ 4 4 | 6 12 6 | 4 12 12 4 | 1 0 4 6 4 1 0 | * * 560 * * * * ♦ 0 0 4 0 0 0 0 | 0 0 6 0 0 0 0 | 0 4 0 0 0
xo3oo .. *b3oo .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 0 1 4 0 0 0 0 | * * * 2240 * * * | 0 0 1 3 0 0 0 | 0 0 3 3 0 0 0 | 0 3 1 0 0
.. oo3ox *b3oo .. .. ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 0 4 0 1 | * * * * 2240 * * | 0 0 1 0 3 0 0 | 0 0 3 0 3 0 0 | 0 3 0 1 0
.o3.o3.x *b3.o .. .. .. ♦ 0 8 | 0 0 24 | 0 0 0 32 | 0 0 0 0 0 8 8 | * * * * * 280 * ♦ 0 0 1 0 0 3 0 | 0 0 3 0 0 3 0 | 0 3 0 0 1
.. .o3.x *b3.o3.o .. .. ♦ 0 5 | 0 0 10 | 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * 1344 | 0 0 0 0 1 1 2 | 0 0 1 0 2 2 1 | 0 2 0 1 1
---------------------------+-------+-------------+---------------------+---------------------------------+---------------------------------+-----------------------------+------------------------+-------------
x.3o.3o. *b3o.3o. .. .. ♦ 16 0 | 80 0 0 | 160 0 0 0 | 40 80 0 0 0 0 0 | 10 16 0 0 0 0 0 | 84 * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0 0
x.3o. .. *b3o.3o.3o. .. ♦ 6 0 | 15 0 0 | 20 0 0 0 | 0 15 0 0 0 0 0 | 0 6 0 0 0 0 0 | * 448 * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0 0
xo3oo3ox *b3oo .. .. ..&#x ♦ 8 8 | 24 32 24 | 32 48 48 32 | 8 8 32 24 32 8 8 | 1 0 8 8 8 1 0 | * * 280 * * * * | 0 0 3 0 0 0 0 | 0 3 0 0 0
xo3oo .. *b3oo3oo .. ..&#x ♦ 5 1 | 10 5 0 | 10 10 0 0 | 0 5 10 0 0 0 0 | 0 1 0 5 0 0 0 | * * * 1344 * * * | 0 0 1 2 0 0 0 | 0 2 1 0 0
.. oo3ox *b3oo3oo .. ..&#x ♦ 1 5 | 0 5 10 | 0 0 10 10 | 0 0 0 0 10 0 5 | 0 0 0 0 5 0 1 | * * * * 1344 * * | 0 0 1 0 2 0 0 | 0 2 0 1 0
.o3.o3.x *b3.o3.o .. .. ♦ 0 16 | 0 0 80 | 0 0 0 160 | 0 0 0 0 0 40 80 | 0 0 0 0 0 10 16 | * * * * * 84 * | 0 0 1 0 0 2 0 | 0 2 0 0 1
.. .o3.x *b3.o3.o3.o .. ♦ 0 6 | 0 0 15 | 0 0 0 20 | 0 0 0 0 0 0 15 | 0 0 0 0 0 0 6 | * * * * * * 448 | 0 0 0 0 1 1 1 | 0 1 0 1 1
---------------------------+-------+-------------+---------------------+---------------------------------+---------------------------------+-----------------------------+------------------------+-------------
x.3o.3o. *b3o.3o.3o. .. ♦ 32 0 | 240 0 0 | 640 0 0 0 | 160 480 0 0 0 0 0 | 60 192 0 0 0 0 0 | 12 32 0 0 0 0 0 | 14 * * * * * * | 1 1 0 0 0
x.3o. .. *b3o.3o.3o.3o. ♦ 7 0 | 21 0 0 | 35 0 0 0 | 0 35 0 0 0 0 0 | 0 21 0 0 0 0 0 | 0 7 0 0 0 0 0 | * 64 * * * * * | 1 0 1 0 0
xo3oo3ox *b3oo3oo .. ..&#x ♦ 16 16 | 80 80 80 | 160 160 160 160 | 40 80 160 80 160 40 80 | 10 16 40 80 80 10 16 | 1 0 10 16 16 1 0 | * * 84 * * * * | 0 2 0 0 0
xo3oo .. *b3oo3oo3oo ..&#x ♦ 6 1 | 15 6 0 | 20 15 0 0 | 0 15 20 0 0 0 0 | 0 6 0 15 0 0 0 | 0 1 0 6 0 0 0 | * * * 448 * * * | 0 1 1 0 0
.. oo3ox *b3oo3oo3oo ..&#x ♦ 1 6 | 0 6 15 | 0 0 15 20 | 0 0 0 0 20 0 15 | 0 0 0 0 15 0 6 | 0 0 0 0 6 0 1 | * * * * 448 * * | 0 1 0 1 0
.o3.o3.x *b3.o3.o3.o .. ♦ 0 32 | 0 0 240 | 0 0 0 640 | 0 0 0 0 0 160 480 | 0 0 0 0 0 60 192 | 0 0 0 0 0 12 32 | * * * * * 14 * | 0 1 0 0 1
.. .o3.x *b3.o3.o3.o3.o ♦ 0 7 | 0 0 21 | 0 0 0 35 | 0 0 0 0 0 0 35 | 0 0 0 0 0 0 21 | 0 0 0 0 0 0 7 | * * * * * * 64 | 0 0 0 1 1
---------------------------+-------+-------------+---------------------+---------------------------------+---------------------------------+-----------------------------+------------------------+-------------
x.3o.3o. *b3o.3o.3o.3o. ♦ 64 0 | 672 0 0 | 2240 0 0 0 | 560 2240 0 0 0 0 0 | 280 1344 0 0 0 0 0 | 84 448 0 0 0 0 0 | 14 64 0 0 0 0 0 | 1 * * * *
xo3oo3ox *b3oo3oo3oo ..&#x ♦ 32 32 | 240 192 240 | 640 480 480 640 | 160 480 640 240 640 160 480 | 60 192 160 480 480 60 192 | 12 32 60 192 192 12 32 | 1 0 12 32 32 1 0 | * 14 * * *
xo3oo .. *b3oo3oo3oo3oo&#x ♦ 7 1 | 21 7 0 | 35 21 0 0 | 0 35 35 0 0 0 0 | 0 21 0 35 0 0 0 | 0 7 0 21 0 0 0 | 0 1 0 7 0 0 0 | * * 64 * *
.. oo3ox *b3oo3oo3oo3oo&#x ♦ 1 7 | 0 7 21 | 0 0 21 35 | 0 0 0 0 35 0 35 | 0 0 0 0 35 0 21 | 0 0 0 0 21 0 7 | 0 0 0 0 7 0 1 | * * * 64 *
.o3.o3.x *b3.o3.o3.o3.o ♦ 0 64 | 0 0 672 | 0 0 0 2240 | 0 0 0 0 0 560 2240 | 0 0 0 0 0 280 1344 | 0 0 0 0 0 84 448 | 0 0 0 0 0 14 64 | * * * * 1
or
o.3o.3o. *b3o.3o.3o.3o. & | 128 ♦ 21 7 | 105 63 | 35 140 140 21 | 35 105 35 175 | 21 42 35 126 | 7 7 21 49 | 1 7 8
-----------------------------+-----+----------+-----------+--------------------+-------------------+------------------+---------------+---------
x. .. .. .. .. .. .. & | 2 | 1344 * ♦ 10 2 | 5 20 10 1 | 10 20 5 20 | 10 10 10 20 | 5 2 10 10 | 1 5 2
oo3oo3oo *b3oo3oo3oo3oo&#x | 2 | * 448 ♦ 0 12 | 0 0 30 6 | 0 0 15 40 | 0 0 20 30 | 0 0 15 12 | 0 6 2
-----------------------------+-----+----------+-----------+--------------------+-------------------+------------------+---------------+---------
x.3o. .. .. .. .. .. & | 3 | 3 0 | 4480 * | 1 4 1 0 | 4 6 1 4 | 6 4 4 6 | 4 1 6 4 | 1 4 1
xo .. .. .. .. .. ..&#x & | 3 | 1 2 | * 2688 | 0 0 5 1 | 0 0 5 10 | 0 0 10 10 | 0 0 10 5 | 0 5 1
-----------------------------+-----+----------+-----------+--------------------+-------------------+------------------+---------------+---------
x.3o.3o. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | 1120 * * * ♦ 4 0 1 0 | 3 0 4 0 | 4 0 6 0 | 1 4 0
x.3o. .. *b3o. .. .. .. & ♦ 4 | 6 0 | 4 0 | * 4480 * * | 1 3 0 1 | 3 3 1 3 | 3 1 3 3 | 1 3 1
xo3oo .. .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * * 4480 * | 0 0 4 1 | 0 0 4 6 | 0 0 6 4 | 0 4 1
xo .. ox .. .. .. ..&#x ♦ 4 | 2 4 | 0 4 | * * * 672 ♦ 0 0 5 0 | 0 0 10 0 | 0 0 10 0 | 0 5 0
-----------------------------+-----+----------+-----------+--------------------+-------------------+------------------+---------------+---------
x.3o.3o. *b3o. .. .. .. & ♦ 8 | 24 0 | 32 0 | 8 8 0 0 | 560 * * * ♦ 3 0 1 0 | 3 0 3 0 | 1 3 0
x.3o. .. *b3o.3o. .. .. & ♦ 5 | 10 0 | 10 0 | 0 5 0 0 | * 2688 * * | 1 2 0 1 | 2 1 1 2 | 1 2 1
xo3oo3ox .. .. .. ..&#x ♦ 8 | 12 12 | 8 24 | 1 0 8 6 | * * 560 * ♦ 0 0 4 0 | 0 0 6 0 | 0 4 0
xo3oo .. *b3oo .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 0 1 4 0 | * * * 4480 | 0 0 1 3 | 0 0 3 3 | 0 3 1
-----------------------------+-----+----------+-----------+--------------------+-------------------+------------------+---------------+---------
x.3o.3o. *b3o.3o. .. .. & ♦ 16 | 80 0 | 160 0 | 40 80 0 0 | 10 16 0 0 | 168 * * * | 2 0 1 0 | 1 2 0
x.3o. .. *b3o.3o.3o. .. & ♦ 6 | 15 0 | 20 0 | 0 15 0 0 | 0 6 0 0 | * 896 * * | 1 1 0 1 | 1 1 1
xo3oo3ox *b3oo .. .. ..&#x ♦ 16 | 48 32 | 64 96 | 16 16 64 24 | 2 0 8 16 | * * 280 * | 0 0 3 0 | 0 3 0
xo3oo .. *b3oo3oo .. ..&#x & ♦ 6 | 10 5 | 10 10 | 0 5 10 0 | 0 1 0 5 | * * * 2688 | 0 0 1 2 | 0 2 1
-----------------------------+-----+----------+-----------+--------------------+-------------------+------------------+---------------+---------
x.3o.3o. *b3o.3o.3o. .. & ♦ 32 | 240 0 | 640 0 | 160 480 0 0 | 60 192 0 0 | 12 32 0 0 | 28 * * * | 1 1 0
x.3o. .. *b3o.3o.3o.3o. & ♦ 7 | 21 0 | 35 0 | 0 35 0 0 | 0 21 0 0 | 0 7 0 0 | * 128 * * | 1 0 1
xo3oo3ox *b3oo3oo .. ..&#x ♦ 32 | 160 80 | 320 320 | 80 160 320 80 | 20 32 40 160 | 2 0 10 32 | * * 84 * | 0 2 0
xo3oo .. *b3oo3oo3oo ..&#x & ♦ 7 | 15 6 | 20 15 | 0 15 20 0 | 0 6 0 15 | 0 1 0 6 | * * * 896 | 0 1 1
-----------------------------+-----+----------+-----------+--------------------+-------------------+------------------+---------------+---------
x.3o.3o. *b3o.3o.3o.3o. & ♦ 64 | 672 0 | 2240 0 | 560 2240 0 0 | 280 1344 0 0 | 84 448 0 0 | 14 64 0 0 | 2 * *
xo3oo3ox *b3oo3oo3oo ..&#x ♦ 64 | 480 192 | 1280 960 | 320 960 1280 240 | 120 384 160 960 | 24 64 60 384 | 2 0 12 64 | * 14 *
xo3oo .. *b3oo3oo3oo3oo&#x & ♦ 8 | 21 7 | 35 21 | 0 35 35 0 | 0 21 0 35 | 0 7 0 21 | 0 1 0 7 | * * 128
xooo3oooo3oxoo3oooo3ooxo3oooo3ooox&#xt → all heights = 1/2
(oca || pseudo broc || pseudo inv. broc || dual oca)
...
ooooo3oxooo3ooooo3ooxoo3ooooo3oooxo3ooooo&#xt → all heights = 1/2
(pt || pseudo roc || pseudo he || pseudo inv. roc || pt)
...
xo3oo3ox *b3oo xo3oo3ox *f3oo&#zx → height = 0
(tegum sum of 2 mutually bigyrated hexdips)
o.3o.3o. *b3o. o.3o.3o. *f3o. & | 128 ♦ 12 16 | 24 144 | 8 8 128 48 144 | 2 32 40 240 36 | 8 48 72 96 | 12 16 56 | 8 8
------------------------------------+-----+----------+-----------+------------------------+----------------------+------------------+------------+-------
x. .. .. .. .. .. .. .. & | 2 | 768 * ♦ 4 8 | 2 2 16 4 12 | 1 8 8 32 6 | 4 16 14 16 | 7 8 12 | 6 2
oo3oo3oo *b3oo oo3oo3oo *f3oo&#x | 2 | * 1024 ♦ 0 12 | 0 0 12 6 18 | 0 6 4 36 18 | 2 18 12 18 | 6 9 12 | 6 2
------------------------------------+-----+----------+-----------+------------------------+----------------------+------------------+------------+-------
x.3o. .. .. .. .. .. .. & | 3 | 3 0 | 1024 * | 1 1 4 0 0 | 1 4 4 6 0 | 4 6 6 4 | 6 4 5 | 5 1
xo .. .. .. .. .. .. ..&#x & | 3 | 1 2 | * 6144 | 0 0 2 1 3 | 0 2 1 9 3 | 1 9 4 6 | 4 6 5 | 5 1
------------------------------------+-----+----------+-----------+------------------------+----------------------+------------------+------------+-------
x.3o.3o. .. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | 256 * * * * ♦ 1 4 0 0 0 | 4 6 0 0 | 6 4 0 | 5 0
x.3o. .. *b3o. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | * 256 * * * | 1 0 4 0 0 | 4 0 6 0 | 6 0 4 | 4 1
xo3oo .. .. .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * * 4096 * * | 0 1 1 3 0 | 1 3 3 3 | 3 3 4 | 4 1
xo .. ox .. .. .. .. ..&#x & ♦ 4 | 2 4 | 0 4 | * * * 1536 * ♦ 0 2 0 0 3 | 1 9 0 0 | 4 6 0 | 5 0
xo .. .. .. .. .. ox ..&#x & ♦ 4 | 2 4 | 0 4 | * * * * 4608 | 0 0 0 4 1 | 0 4 2 4 | 2 4 4 | 4 1
------------------------------------+-----+----------+-----------+------------------------+----------------------+------------------+------------+-------
x.3o.3o. *b3o. .. .. .. .. & ♦ 8 | 24 0 | 32 0 | 8 8 0 0 0 | 32 * * * * ♦ 4 0 0 0 | 6 0 0 | 4 0
xo3oo3ox .. .. .. .. ..&#x & ♦ 8 | 12 12 | 8 24 | 2 0 8 6 0 | * 512 * * * ♦ 1 3 0 0 | 3 3 0 | 4 0
xo3oo .. *b3oo .. .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 0 1 4 0 0 | * * 1024 * * | 1 0 3 0 | 3 0 3 | 3 1
xo3oo .. .. .. .. ox ..&#x & ♦ 5 | 4 6 | 1 9 | 0 0 2 0 3 | * * * 6144 * | 0 1 1 2 | 1 2 3 | 3 1
xo .. ox .. xo .. ox ..&#zx ♦ 8 | 8 16 | 0 32 | 0 0 0 8 8 | * * * * 576 ♦ 0 4 0 0 | 2 4 0 | 4 0
------------------------------------+-----+----------+-----------+------------------------+----------------------+------------------+------------+-------
xo3oo3ox *b3oo .. .. .. ..&#x & ♦ 16 | 48 32 | 64 96 | 16 16 64 24 0 | 2 8 16 0 0 | 64 * * * | 3 0 0 | 3 0
xo3oo3ox .. xo .. ox ..&#zx & ♦ 16 | 32 48 | 16 144 | 4 0 32 36 48 | 0 4 0 16 6 | * 384 * * | 1 2 0 | 3 0
xo3oo .. *b3oo .. .. ox ..&#x & ♦ 6 | 7 8 | 4 16 | 0 1 8 0 6 | 0 0 2 4 0 | * * 1536 * | 1 0 2 | 2 1
xo3oo .. .. .. oo3ox ..&#x & ♦ 6 | 6 9 | 2 18 | 0 0 6 0 9 | 0 0 0 6 0 | * * * 2048 | 0 1 2 | 2 1
------------------------------------+-----+----------+-----------+------------------------+----------------------+------------------+------------+-------
xo3oo3ox *b3oo xo .. ox ..&#zx & ♦ 32 | 112 128 | 128 512 | 32 32 256 128 192 | 4 32 64 128 24 | 4 8 32 0 | 48 * * | 2 0
xo3oo3ox .. xo3oo3ox ..&#zx ♦ 32 | 96 144 | 64 576 | 16 0 192 144 288 | 0 24 0 192 36 | 0 12 0 32 | * 64 * | 2 0
xo3oo .. *b3oo .. oo3ox ..&#x & ♦ 7 | 9 12 | 5 30 | 0 1 16 0 18 | 0 0 3 18 0 | 0 0 3 4 | * * 1024 | 1 1
------------------------------------+-----+----------+-----------+------------------------+----------------------+------------------+------------+-------
xo3oo3ox *b3oo xo3oo3ox ..&#zx & ♦ 64 | 288 384 | 320 1920 | 80 64 1024 480 1152 | 8 128 192 1152 144 | 12 72 192 256 | 6 8 64 | 16 *
xo3oo .. *b3oo .. oo3ox *f3oo&#x & ♦ 8 | 12 16 | 8 48 | 0 2 32 0 36 | 0 0 8 48 0 | 0 0 12 16 | 0 0 8 | * 128