Acronym | naq (alt: rocalroc) | ||||||||||||||||
Name |
hecatonicosihexapentacosiheptacontihexaexon, sideroexon, Gosset polyexon 32,1, alterelongated jak tegum, vertex figure of fy, (one of the) Delone cell(s) of lattice E7, tegum sum of 2 mutually inverted rectified octaexa, biambohexadecaexon, lattice E7* contact polytope (span of its roots) | ||||||||||||||||
Circumradius | sqrt(3)/2 = 0.866025 | ||||||||||||||||
Inradius wrt. hop | 3/sqrt(28) = 0.566947 | ||||||||||||||||
Inradius wrt. gee | 1/2 = 0.5 | ||||||||||||||||
Lace city in approx. ASCII-art |
o T o ------ o3o3o *b3o3o3x (gee) N n \----- x3o3o *b3o3o3o (hax) \ o T o --\--- o3o3o *b3o3o3x (gee) \ \ \ \ +- o3o3o3o3o *c3o (point) \ \ +----- x3o3o3o3o *c3o (jak) \ +---------- o3o3o3o3x *c3o (alt. jak) +--------------- o3o3o3o3o *c3o (point) where: o = o3o3o *b3o3o (point) T = o3o3o *b3o3x (tac) N = x3o3o *b3o3o (hin) n = o3o3x *b3o3o (alternate hin) | ||||||||||||||||
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_+------- x3o3o3o3o3o (hop) _- _+----- o3o3o3o3x3o (inv ril) _- _- _+--- o3x3o3o3o3o (ril) _- _- _- _+- o3o3o3o3o3x (dual hop) o -- o3o3o3o3o *c3o (point) h R h -- x3o3o3o3o *c3o (jak) H r H -- o3o3o3o3x *c3o (alt. jak) o -- o3o3o3o3o *c3o (point) | | +- o3o3o *b3o3o3x (gee) | +------ x3o3o *b3o3o3o (hax) +----------- o3o3o *b3o3o3x (gee) where: o = o3o3o3o3o (point) h = x3o3o3o3o (hix) H = o3o3o3o3x (dual hix) r = o3x3o3o3o (rix) R = o3o3o3x3o (inv rix) | |||||||||||||||||
Lace hyper city in approx. ASCII-art |
_ p-------------p / N _/ | p-----+-------p | | O| | | E | | E | | O | | | _ p - - - + - - p | / N | _/ p-------------p where: p = o3o3o *b3o (point) N = x3o3o *b3o (hex) E = o3o3x *b3o (gyro hex) O = o3o3o *b3x (alt. gyro hex) thus vertically: o3o3o *b3o3o3x (gee) || x3o3o *b3o3o3o (hax) || o3o3o *b3o3o3x (gee) or diametrically: o3o3o3o3o *c3o (point) || x3o3o3o3o *c3o (jak) || o3o3o3o3x *c3o alt. jak || o3o3o3o3o *c3o (point) or face-diagonally: x o3o3o *c3o3o (line) || o x3o3o *c3o3o (perp hin) || x o3o3o *c3o3x (taccup) || o o3o3x *c3o3o (perp alt hin) || x o3o3o *c3o3o (line) | ||||||||||||||||
Coordinates |
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Volume | 17/140 = 0.121429 | ||||||||||||||||
Surface | [14+sqrt(7)]/10 = 1.664575 | ||||||||||||||||
Dihedral angles | |||||||||||||||||
General of army | (is itself convex) | ||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polyexal members:
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Face vector | 56, 756, 4032, 10080, 12096, 6048, 702 | ||||||||||||||||
Confer | |||||||||||||||||
External links |
This polyexon belongs to E7 symmetry. When considered in axial E6 subsymmetry, it will be displayed vertex first. Then its medial segment is jaka. Alternatively it can be oriented in axial A6 subsymmetry, where it will be displayed hop facet first. Then its medial segment is rila. Both representations are tristratic. In axial D6 subsymmetry it will be displayed gee facet first and is bistratic only.
Wrt. A7 subsymmetry naq can be thought of as a tegum sum of 2 inverse
rocs. In fact, it happens to be the hull of rush, the according
compound or, alternatively, the hull of the degenerate polyzetton roca
Wrt. D4 × A1 × A1 × A1 subsymmetry naq can be thought of as a tegum sum
of 3 mutually gyrated, lacings-orthogonal hexips and a cube within lacings subspace only.
From the above high symmetrical vertex subsets by combination further at least orbiform vertex inscribed polytopes are derivable:
Incidence matrix according to Dynkin symbol
o3o3o3o *c3o3o3x . . . . . . . | 56 ♦ 27 | 216 | 720 | 1080 | 432 216 | 72 27 -----------------+----+-----+------+-------+-------+-----------+-------- . . . . . . x | 2 | 756 ♦ 16 | 80 | 160 | 80 40 | 16 10 -----------------+----+-----+------+-------+-------+-----------+-------- . . . . . o3x | 3 | 3 | 4032 ♦ 10 | 30 | 20 10 | 5 5 -----------------+----+-----+------+-------+-------+-----------+-------- . . . . o3o3x ♦ 4 | 6 | 4 | 10080 ♦ 6 | 6 3 | 2 3 -----------------+----+-----+------+-------+-------+-----------+-------- . . o . *c3o3o3x ♦ 5 | 10 | 10 | 5 | 12096 | 2 1 | 1 2 -----------------+----+-----+------+-------+-------+-----------+-------- . o3o . *c3o3o3x ♦ 6 | 15 | 20 | 15 | 6 | 4032 * | 1 1 . . o3o *c3o3o3x ♦ 6 | 15 | 20 | 15 | 6 | * 2016 | 0 2 -----------------+----+-----+------+-------+-------+-----------+-------- o3o3o . *c3o3o3x ♦ 7 | 21 | 35 | 35 | 21 | 7 0 | 576 * . o3o3o *c3o3o3x ♦ 12 | 60 | 160 | 240 | 192 | 32 32 | * 126
oxo3ooo3ooo *b3ooo3ooo3xox&#xt → both heights = 1/2 (gee || pseudo hax || gee) o..3o..3o.. *b3o..3o..3o.. & | 24 * ♦ 10 16 1 0 | 40 80 80 16 0 | 80 160 240 160 80 0 0 | 80 40 80 320 240 160 160 0 | 16 16 16 80 80 160 80 80 40 80 0 | 1 40 16 16 10 16 .o.3.o.3.o. *b3.o.3.o.3.o. | * 32 ♦ 0 12 0 15 | 0 120 30 6 60 | 0 360 180 40 60 20 60 | 0 120 240 360 120 30 180 30 | 0 0 60 120 120 120 30 12 60 120 6 | 0 40 12 2 15 30 ---------------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- ... ... ... ... ... x.. & | 2 0 | 120 * * * ♦ 8 0 8 0 0 | 24 0 24 32 0 0 0 | 32 0 0 32 48 48 0 0 | 8 8 0 8 8 32 24 32 0 0 0 | 1 8 8 8 1 0 oo.3oo.3oo. *b3oo.3oo.3oo.&#x & | 1 1 | * 384 * * ♦ 0 10 5 1 0 | 0 30 30 10 10 0 0 | 0 10 20 60 30 10 30 0 | 0 0 5 20 20 30 10 5 10 20 0 | 0 10 5 1 5 5 o.o3o.o3o.o *b3o.o3o.o3o.o&#x & | 2 0 | * * 12 * ♦ 0 0 0 16 0 | 0 0 0 0 80 0 0 | 0 0 0 0 0 0 160 0 | 0 0 0 0 0 0 0 0 40 80 0 | 0 0 0 0 10 16 .x. ... ... ... ... ... | 0 2 | * * * 240 ♦ 0 8 0 0 8 | 0 48 12 0 4 4 12 | 0 24 48 48 8 0 24 8 | 0 0 16 24 24 16 2 0 12 24 2 | 0 8 4 0 6 8 ---------------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- ... ... ... ... o..3x.. & | 3 0 | 3 0 0 0 | 320 * * * * ♦ 6 0 0 4 0 0 0 | 12 0 0 0 6 12 0 0 | 4 4 0 0 0 4 6 12 0 0 0 | 1 1 4 4 0 0 ox. ... ... ... ... ...&#x & | 1 2 | 0 2 0 1 | * 1920 * * * ♦ 0 6 3 0 1 0 0 | 0 3 6 12 3 0 6 0 | 0 0 2 6 6 6 1 0 3 6 0 | 0 3 2 0 3 2 ... ... ... ... ... xo.&#x & | 2 1 | 1 2 0 0 | * * 960 * * ♦ 0 0 6 4 0 0 0 | 0 0 0 12 12 6 0 0 | 0 0 0 4 4 12 6 4 0 0 0 | 0 4 4 1 1 0 ooo3ooo3ooo *b3ooo3ooo3ooo&#x & | 2 1 | 0 2 1 0 | * * * 192 * ♦ 0 0 0 0 10 0 0 | 0 0 0 0 0 0 30 0 | 0 0 0 0 0 0 0 0 10 20 0 | 0 0 0 0 5 5 .x.3.o. ... ... ... ... | 0 3 | 0 0 0 3 | * * * * 640 ♦ 0 6 0 0 0 1 3 | 0 6 12 6 0 0 3 3 | 0 0 6 6 6 2 0 0 3 6 1 | 0 2 2 0 3 3 ---------------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- ... ... ... o..3o..3x.. & ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | 480 * * * * * * ♦ 4 0 0 0 0 2 0 0 | 2 2 0 0 0 0 1 4 0 0 0 | 1 0 2 2 0 0 ox.3oo. ... ... ... ...&#x & ♦ 1 3 | 0 3 0 3 | 0 3 0 0 1 | * 3840 * * * * * ♦ 0 1 2 2 0 0 1 0 | 0 0 1 2 2 1 0 0 1 2 0 | 0 1 1 0 2 1 ox. ... ... ... ... xo.&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 | * * 2880 * * * * ♦ 0 0 0 4 2 0 0 0 | 0 0 0 2 2 4 1 0 0 0 0 | 0 2 2 0 1 0 ... ... ... ... oo.3xo.&#x & ♦ 3 1 | 3 3 0 0 | 1 0 3 0 0 | * * * 1280 * * * ♦ 0 0 0 0 3 3 0 0 | 0 0 0 0 0 3 3 3 0 0 0 | 0 1 3 1 0 0 oxo ... ... ... ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 2 0 2 0 | * * * * 960 * * ♦ 0 0 0 0 0 0 6 0 | 0 0 0 0 0 0 0 0 3 6 0 | 0 0 0 0 3 2 .x.3.o.3.o. ... ... ... ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * 160 * ♦ 0 6 0 0 0 0 0 0 | 0 0 0 6 0 0 0 0 3 0 0 | 0 2 0 0 3 0 .x.3.o. ... *b3.o. ... ... ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * * 480 ♦ 0 0 4 0 0 0 0 2 | 0 0 4 0 2 0 0 0 0 2 1 | 0 0 2 0 1 2 ---------------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- ... o.. ... *b3o..3o..3x.. & ♦ 5 0 | 10 0 0 0 | 10 0 0 0 0 | 5 0 0 0 0 0 0 | 384 * * * * * * * | 1 1 0 0 0 0 0 1 0 0 0 | 1 0 1 1 0 0 ox.3oo.3oo. ... ... ...&#x & ♦ 1 4 | 0 4 0 6 | 0 6 0 0 4 | 0 4 0 0 0 1 0 | * 960 * * * * * * | 0 0 0 2 0 0 0 0 1 0 0 | 0 1 0 0 2 0 ox.3oo. ... *b3oo. ... ...&#x & ♦ 1 4 | 0 4 0 6 | 0 6 0 0 4 | 0 4 0 0 0 0 1 | * * 1920 * * * * * | 0 0 1 0 1 0 0 0 0 1 0 | 0 0 1 0 1 1 ox.3oo. ... ... ... xo.&#x & ♦ 2 3 | 1 6 0 3 | 0 6 3 0 1 | 0 2 3 0 0 0 0 | * * * 3840 * * * * | 0 0 0 1 1 1 0 0 0 0 0 | 0 1 1 0 1 0 ox. ... ... ... oo.3xo.&#x & ♦ 3 2 | 3 6 0 1 | 1 3 6 0 0 | 0 0 3 2 0 0 0 | * * * * 1920 * * * | 0 0 0 0 0 2 1 0 0 0 0 | 0 1 2 0 0 0 ... ... ... oo.3oo.3xo.&#x & ♦ 4 1 | 6 4 0 0 | 4 0 6 0 0 | 1 0 0 4 0 0 0 | * * * * * 960 * * | 0 0 0 0 0 0 1 2 0 0 0 | 0 0 2 1 0 0 oxo3ooo ... ... ... ...&#x ♦ 2 3 | 0 6 1 3 | 0 6 0 3 1 | 0 2 0 0 3 0 0 | * * * * * * 1920 * | 0 0 0 0 0 0 0 0 1 2 0 | 0 0 0 0 2 1 .x.3.o. ... *b3.o.3.o. ... ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * * 192 | 0 0 2 0 0 0 0 0 0 0 1 | 0 0 2 0 0 1 ---------------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- o..3o.. ... *b3o..3o..3x.. & ♦ 6 0 | 15 0 0 0 | 20 0 0 0 0 | 15 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 | 64 * * * * * * * * * * | 1 0 1 0 0 0 ... o..3o.. *b3o..3o..3x.. & ♦ 6 0 | 15 0 0 0 | 20 0 0 0 0 | 15 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 | * 64 * * * * * * * * * | 1 0 0 1 0 0 ox.3oo. ... *b3oo.3oo. ...&#x & ♦ 1 5 | 0 5 0 10 | 0 10 0 0 10 | 0 10 0 0 0 0 5 | 0 0 5 0 0 0 0 1 | * * 384 * * * * * * * * | 0 0 1 0 0 1 ox.3oo.3oo. ... ... xo.&#x & ♦ 2 4 | 1 8 0 6 | 0 12 4 0 4 | 0 8 6 0 0 1 0 | 0 2 0 4 0 0 0 0 | * * * 960 * * * * * * * | 0 1 0 0 1 0 ox.3oo. ... *b3oo. ... xo.&#x & ♦ 2 4 | 1 8 0 6 | 0 12 4 0 4 | 0 8 6 0 0 0 1 | 0 0 2 4 0 0 0 0 | * * * * 960 * * * * * * | 0 0 1 0 1 0 ox.3oo. ... ... oo.3xo.&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 1 | 0 3 9 3 0 0 0 | 0 0 0 3 3 0 0 0 | * * * * * 1280 * * * * * | 0 1 1 0 0 0 ox. ... ... oo.3oo.3xo.&#x & ♦ 4 2 | 6 8 0 1 | 4 4 12 0 0 | 1 0 6 8 0 0 0 | 0 0 0 0 4 2 0 0 | * * * * * * 480 * * * * | 0 0 2 0 0 0 ... oo. ... *b3oo.3oo.3xo.&#x & ♦ 5 1 | 10 5 0 0 | 10 0 10 0 0 | 5 0 0 10 0 0 0 | 1 0 0 0 0 5 0 0 | * * * * * * * 384 * * * | 0 0 1 1 0 0 oxo3ooo3ooo ... ... ...&#x ♦ 2 4 | 0 8 1 6 | 0 12 0 4 4 | 0 8 0 0 6 1 0 | 0 2 0 0 0 0 4 0 | * * * * * * * * 480 * * | 0 0 0 0 2 0 oxo3ooo ... *b3ooo ... ...&#x ♦ 2 4 | 0 8 1 6 | 0 12 0 4 4 | 0 8 0 0 6 0 1 | 0 0 2 0 0 0 4 0 | * * * * * * * * * 960 * | 0 0 0 0 1 1 .x.3.o. ... *b3.o.3.o.3.o. ♦ 0 6 | 0 0 0 15 | 0 0 0 0 20 | 0 0 0 0 0 0 15 | 0 0 0 0 0 0 0 6 | * * * * * * * * * * 32 | 0 0 2 0 0 0 ---------------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- o..3o..3o.. *b3o..3o..3x.. & ♦ 12 0 | 60 0 0 0 | 160 0 0 0 0 | 240 0 0 0 0 0 0 | 192 0 0 0 0 0 0 0 | 32 32 0 0 0 0 0 0 0 0 0 | 2 * * * * * ox.3oo.3oo. ... oo.3xo.&#x & ♦ 3 4 | 3 12 0 6 | 1 18 12 0 4 | 0 12 18 4 0 1 0 | 0 3 0 12 6 0 0 0 | 0 0 0 3 0 4 0 0 0 0 0 | * 320 * * * * ox.3oo. ... *b3oo.3oo.3xo.&#x & ♦ 6 6 | 15 30 0 15 | 20 60 60 0 20 | 15 60 90 60 0 0 15 | 6 0 30 60 60 30 0 6 | 1 0 6 0 15 20 15 6 0 0 1 | * * 64 * * * ... oo.3oo. *b3oo.3oo.3xo.&#x & ♦ 6 1 | 15 6 0 0 | 20 0 15 0 0 | 15 0 0 20 0 0 0 | 6 0 0 0 0 15 0 0 | 0 1 0 0 0 0 0 6 0 0 0 | * * * 64 * * oxo3ooo3ooo *b3ooo ... xox&#x ♦ 4 8 | 2 32 2 24 | 0 96 16 16 32 | 0 128 48 0 48 8 8 | 0 32 32 64 0 0 64 0 | 0 0 0 16 16 0 0 0 16 16 0 | * * * * 60 * oxo3ooo ... *b3ooo3ooo ...&#x ♦ 2 5 | 0 10 1 10 | 0 20 0 5 10 | 0 20 0 0 10 0 5 | 0 0 10 0 0 0 10 1 | 0 0 2 0 0 0 0 0 0 5 0 | * * * * * 192
oxoo3oooo3oooo3oooo3ooxo *c3oooo&#xt → all heights = 1/sqrt(3) = 0.577350 (pt || pseudo jak || pseudo alt. jak || pt) o...3o...3o...3o...3o... *c3o... & | 2 * ♦ 27 0 0 | 216 0 0 | 720 0 0 0 | 1080 0 0 0 0 | 432 216 0 0 0 0 0 | 72 27 0 0 .o..3.o..3.o..3.o..3.o.. *c3.o.. & | * 54 ♦ 1 16 10 | 16 80 120 | 80 160 320 160 | 160 80 40 400 400 | 80 40 16 96 240 96 80 | 16 11 16 56 ---------------------------------------+------+------------+---------------+---------------------+------------------------+------------------------------+-------------- oo..3oo..3oo..3oo..3oo.. *c3oo..&#x & | 1 1 | 54 * * ♦ 16 0 0 | 80 0 0 0 | 160 0 0 0 0 | 80 40 0 0 0 0 0 | 16 10 0 0 .x.. .... .... .... .... .... & | 0 2 | * 432 * ♦ 1 10 5 | 10 30 30 10 | 30 20 10 60 40 | 20 10 5 20 35 20 10 | 5 5 5 11 .oo.3.oo.3.oo.3.oo.3.oo. *c3.oo.&#x | 0 2 | * * 270 ♦ 0 0 16 | 0 0 48 32 | 0 0 0 64 96 | 0 0 0 16 64 16 24 | 0 2 8 16 ---------------------------------------+------+------------+---------------+---------------------+------------------------+------------------------------+-------------- ox.. .... .... .... .... ....&#x & | 1 2 | 2 1 0 | 432 * * ♦ 10 0 0 0 | 30 0 0 0 0 | 20 10 0 0 0 0 0 | 5 5 0 0 .x..3.o.. .... .... .... .... & | 0 3 | 0 3 0 | * 1440 * ♦ 1 6 3 0 | 6 6 3 12 3 | 6 3 2 6 6 6 1 | 2 3 2 3 .xo. .... .... .... .... ....&#x & | 0 3 | 0 1 2 | * * 2160 ♦ 0 0 6 4 | 0 0 0 12 18 | 0 0 0 4 16 4 6 | 0 1 4 5 ---------------------------------------+------+------------+---------------+---------------------+------------------------+------------------------------+-------------- ox..3oo.. .... .... .... ....&#x & ♦ 1 3 | 3 3 0 | 3 1 0 | 1440 * * * ♦ 6 0 0 0 0 | 6 3 0 0 0 0 0 | 2 3 0 0 .x..3.o..3.o.. .... .... .... & ♦ 0 4 | 0 6 0 | 0 4 0 | * 2160 * * ♦ 1 2 1 2 0 | 2 1 1 2 1 2 0 | 1 2 1 1 .xo.3.oo. .... .... .... ....&#x & ♦ 0 4 | 0 3 3 | 0 1 3 | * * 4320 * ♦ 0 0 0 4 2 | 0 0 0 2 4 2 1 | 0 1 2 2 .xo. .... .... .... .ox. ....&#x ♦ 0 4 | 0 2 4 | 0 0 4 | * * * 2160 ♦ 0 0 0 0 6 | 0 0 0 0 6 0 3 | 0 0 3 2 ---------------------------------------+------+------------+---------------+---------------------+------------------------+------------------------------+-------------- ox..3oo..3oo.. .... .... ....&#x & ♦ 1 4 | 4 6 0 | 6 4 0 | 4 1 0 0 | 2160 * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 .x..3.o..3.o..3.o.. .... .... & ♦ 0 5 | 0 10 0 | 0 10 0 | 0 5 0 0 | * 864 * * * | 1 0 1 1 0 0 0 | 1 1 1 0 .x..3.o..3.o.. .... .... *c3.o.. & ♦ 0 5 | 0 10 0 | 0 10 0 | 0 5 0 0 | * * 432 * * | 0 1 0 0 0 2 0 | 0 2 0 1 .xo.3.oo.3.oo. .... .... ....&#x & ♦ 0 5 | 0 6 4 | 0 4 6 | 0 1 4 0 | * * * 4320 * | 0 0 0 1 1 1 0 | 0 1 1 1 .xo.3.oo. .... .... .ox. ....&#x & ♦ 0 5 | 0 4 6 | 0 1 9 | 0 0 2 3 | * * * * 4320 | 0 0 0 0 2 0 1 | 0 0 2 1 ---------------------------------------+------+------------+---------------+---------------------+------------------------+------------------------------+-------------- ox..3oo..3oo..3oo.. .... ....&#x & ♦ 1 5 | 5 10 0 | 10 10 0 | 10 5 0 0 | 5 1 0 0 0 | 864 * * * * * * | 1 1 0 0 ox..3oo..3oo.. .... .... *c3oo..&#x & ♦ 1 5 | 5 10 0 | 10 10 0 | 10 5 0 0 | 5 0 1 0 0 | * 432 * * * * * | 0 2 0 0 .x..3.o..3.o..3.o..3.o.. .... & ♦ 0 6 | 0 15 0 | 0 20 0 | 0 15 0 0 | 0 6 0 0 0 | * * 144 * * * * | 1 0 1 0 .xo.3.oo.3.oo.3.oo. .... ....&#x & ♦ 0 6 | 0 10 5 | 0 10 10 | 0 5 10 0 | 0 1 0 5 0 | * * * 864 * * * | 0 1 1 0 .xo.3.oo.3.oo. .... .ox. ....&#x & ♦ 0 6 | 0 7 8 | 0 4 16 | 0 1 8 6 | 0 0 0 2 4 | * * * * 2160 * * | 0 0 1 1 .xo.3.oo.3.oo. .... .... *c3.oo.&#x & ♦ 0 6 | 0 10 5 | 0 10 10 | 0 5 10 0 | 0 0 1 5 0 | * * * * * 864 * | 0 1 0 1 .xo.3.oo. .... .oo.3.ox. ....&#x ♦ 0 6 | 0 6 9 | 0 2 18 | 0 0 6 9 | 0 0 0 0 6 | * * * * * * 720 | 0 0 2 0 ---------------------------------------+------+------------+---------------+---------------------+------------------------+------------------------------+-------------- ox..3oo..3oo..3oo..3oo.. ....&#x & ♦ 1 6 | 6 15 0 | 15 20 0 | 20 15 0 0 | 15 6 0 0 0 | 6 0 1 0 0 0 0 | 144 * * * oxo.3ooo.3ooo.3ooo. .... *c3ooo.&#xt & ♦ 1 11 | 10 40 10 | 40 80 40 | 80 80 80 0 | 80 16 16 80 0 | 16 16 0 16 0 16 0 | * 54 * * .xo.3.oo.3.oo.3.oo.3.ox. ....&#x ♦ 0 12 | 0 30 30 | 0 40 120 | 0 30 120 90 | 0 12 0 60 120 | 0 0 2 12 30 0 20 | * * 72 * .xo.3.oo.3.oo. .... .ox. *c3.oo.&#x & ♦ 0 7 | 0 11 10 | 0 10 25 | 0 5 20 10 | 0 0 1 10 10 | 0 0 0 0 5 2 0 | * * * 432
xoxox oxooo3ooooo3oooxo *c3ooooo3ooxoo&#xt → all heights = 1/sqrt(8) = 0.353553 (line || pseudo perp hin || pseudo taccup || pseudo perp alt hin || line) o.... o....3o....3o.... *c3o....3o.... & | 4 * * ♦ 1 16 10 0 0 0 0 0 | 16 80 40 80 0 0 0 0 0 0 0 | 80 160 80 240 160 0 0 0 0 0 0 0 0 0 0 0 0 | 160 40 80 80 320 240 160 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 40 80 16 16 16 80 80 160 80 80 0 0 0 0 0 0 0 0 0 0 0 0 | 16 10 16 1 40 16 0 0 0 .o... .o...3.o...3.o... *c3.o...3.o... & | * 32 * ♦ 0 2 0 10 10 5 0 0 | 1 20 0 10 30 5 60 20 30 40 0 | 10 60 0 60 20 10 20 30 120 60 20 40 10 20 180 60 0 | 30 20 40 0 120 60 20 5 60 40 40 60 20 10 25 90 160 60 180 40 0 | 10 20 10 0 0 40 40 60 20 10 20 20 20 2 6 80 30 60 50 80 60 10 | 5 5 12 0 20 2 10 25 20 ..o.. ..o..3..o..3..o.. *c3..o..3..o.. | * * 20 ♦ 0 0 2 0 16 0 1 8 | 0 0 16 16 0 16 48 64 0 32 24 | 0 0 48 48 64 0 0 48 64 96 96 0 0 32 96 96 32 | 0 0 0 64 64 96 96 0 64 16 16 64 48 64 0 96 64 24 192 96 16 | 0 0 0 16 16 16 16 64 48 64 16 16 16 16 0 64 24 48 16 64 96 32 | 0 2 16 1 16 16 8 16 24 ---------------------------------------------+---------+--------------------------+--------------------------------------------+---------------------------------------------------------------------+--------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+----------------------------- x.... ..... ..... ..... ..... ..... & | 2 0 0 | 2 * * * * * * * ♦ 32 0 0 0 0 0 0 0 0 0 0 | 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 160 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 40 80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 16 10 0 0 0 0 0 0 0 oo... oo...3oo...3oo... *c3oo...3oo...&#x & | 1 1 0 | * 64 * * * * * * ♦ 1 10 0 5 0 0 0 0 0 0 0 | 10 30 0 30 10 0 0 0 0 0 0 0 0 0 0 0 0 | 30 10 20 0 60 30 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10 20 5 0 0 20 20 30 10 5 0 0 0 0 0 0 0 0 0 0 0 0 | 5 5 5 0 10 1 0 0 0 o.o.. o.o..3o.o..3o.o.. *c3o.o..3o.o..&#x & | 1 0 1 | * * 40 * * * * * ♦ 0 0 8 8 0 0 0 0 0 0 0 | 0 0 24 24 32 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 32 32 48 48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 8 8 8 8 32 24 32 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 8 1 8 8 0 0 0 ..... .x... ..... ..... ..... ..... & | 0 2 0 | * * * 160 * * * * ♦ 0 2 0 0 6 0 6 0 2 0 0 | 1 12 0 6 0 3 6 3 24 6 0 6 1 0 12 0 0 | 6 6 12 0 24 6 0 2 12 12 12 12 2 0 6 6 24 6 12 0 0 | 3 6 4 0 0 12 12 12 2 0 6 6 6 0 2 12 3 6 12 12 4 0 | 2 3 4 0 6 0 3 6 2 .oo.. .oo..3.oo..3.oo.. *c3.oo..3.oo..&#x & | 0 1 1 | * * * * 320 * * * ♦ 0 0 0 1 0 1 6 4 0 4 0 | 0 0 0 6 4 0 0 6 12 12 6 0 0 4 18 12 0 | 0 0 0 0 12 12 6 0 12 4 4 12 6 4 0 18 16 12 36 12 0 | 0 0 0 0 0 4 4 12 6 4 4 4 4 1 0 12 6 12 5 12 18 4 | 0 1 5 0 4 1 4 5 6 .o.o. .o.o.3.o.o.3.o.o. *c3.o.o.3.o.o.&#x | 0 2 0 | * * * * * 80 * * ♦ 0 0 0 0 0 0 0 0 8 8 0 | 0 0 0 0 0 0 0 0 0 0 0 12 4 4 48 12 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 24 48 24 48 8 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 24 12 24 16 24 16 2 | 0 0 4 0 0 0 6 8 8 ..x.. ..... ..... ..... ..... ..... | 0 0 2 | * * * * * * 10 * ♦ 0 0 0 0 0 16 0 0 0 0 0 | 0 0 0 0 0 0 0 48 0 0 0 0 0 32 0 0 0 | 0 0 0 0 0 0 0 0 64 0 0 0 0 0 0 96 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 16 16 0 0 0 64 24 0 0 0 0 0 | 0 2 0 0 0 0 8 16 0 ..... ..... ..... ..... ..... ..x.. | 0 0 2 | * * * * * * * 80 ♦ 0 0 2 0 0 0 0 8 0 0 6 | 0 0 12 0 8 0 0 0 0 12 24 0 0 0 0 12 12 | 0 0 0 24 0 12 24 0 0 0 0 8 12 24 0 0 0 0 24 24 8 | 0 0 0 8 8 0 0 8 12 24 0 0 2 8 0 0 0 6 0 8 24 12 | 0 0 8 1 2 8 1 0 6 ---------------------------------------------+---------+--------------------------+--------------------------------------------+---------------------------------------------------------------------+--------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+----------------------------- xo... ..... ..... ..... ..... .....&#x & | 2 1 0 | 1 2 0 0 0 0 0 0 | 32 * * * * * * * * * * ♦ 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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| 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 | 0 0 0 0 0 1 2 0 .... oox. .... .... oxo. ....&#x & ♦ 1 4 | 0 2 2 2 4 | 0 0 1 0 1 4 0 0 4 | 0 0 0 0 0 0 0 2 2 0 0 0 1 | * * * * * * * * * 2520 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 0 0 0 1 1 1 .... .... .... ooo.3oxo. ....&#x & ♦ 1 4 | 0 3 1 3 3 | 0 0 3 0 0 3 1 0 3 | 0 0 0 1 0 0 0 0 3 0 0 1 0 | * * * * * * * * * * 1680 * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 | 0 0 0 0 1 0 1 1 .... .... .... .... oxo.3ooo.&#x & ♦ 1 4 | 0 3 1 3 3 | 0 0 3 0 0 3 0 1 3 | 0 0 0 0 1 0 0 0 3 0 1 0 0 | * * * * * * * * * * * 840 * * * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 | 0 0 0 0 0 1 0 2 .... .o..3.o..3.o..3.x.. .... & ♦ 0 5 | 0 0 0 10 0 | 0 0 0 0 0 0 10 0 0 | 0 0 0 0 0 0 0 0 0 5 0 0 0 | * * * * * * * * * * * * 84 * * * | 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 | 0 1 0 1 0 0 1 0 .oo.3.ox. .... .... .xo. ....&#x & ♦ 0 5 | 0 0 0 4 6 | 0 0 0 0 0 0 0 1 9 | 0 0 0 0 0 0 0 0 0 0 2 0 3 | * * * * * * * * * * * * * 840 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 0 0 1 0 2 .... .ox.3.oo.3.oo. .... ....&#x & ♦ 0 5 | 0 0 0 6 4 | 0 0 0 0 0 0 4 0 6 | 0 0 0 0 0 0 0 0 0 1 0 4 0 | * * * * * * * * * * * * * * 210 * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 | 0 0 0 0 1 0 2 0 .... .ox.3.oo. .... .xo. ....&#x & ♦ 0 5 | 0 0 0 4 6 | 0 0 0 0 0 0 1 0 9 | 0 0 0 0 0 0 0 0 0 0 0 2 3 | * * * * * * * * * * * * * * * 840 | 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 | 0 0 0 0 0 1 1 1 ------------------------------------+-------+-------------------+-----------------------------------+--------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------------+------------------------- x...3o...3o...3o...3o... .... & ♦ 6 0 | 15 0 0 0 0 | 20 0 0 0 0 0 0 0 0 | 15 0 0 0 0 0 0 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 14 * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 xo..3oo..3oo..3oo.. .... ....&#x & ♦ 5 1 | 10 5 0 0 0 | 10 10 0 0 0 0 0 0 0 | 5 10 0 0 0 0 0 0 0 0 0 0 0 | 1 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 42 * * * * * * * * * * * * * * * * | 0 2 0 0 0 0 0 0 xo..3oo..3oo.. .... ox.. ....&#x & ♦ 4 2 | 6 8 0 1 0 | 4 12 4 0 0 0 0 0 0 | 1 8 6 0 0 0 0 0 0 0 0 0 0 | 0 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 210 * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 xo..3oo.. .... oo..3ox.. ....&#x & ♦ 3 3 | 3 9 0 3 0 | 1 9 9 0 0 0 1 0 0 | 0 3 9 3 0 0 0 0 0 0 0 0 0 | 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 280 * * * * * * * * * * * * * * | 0 1 0 0 0 0 0 1 xo..3oo.. .... .... ox..3oo..&#x & ♦ 3 3 | 3 9 0 3 0 | 1 9 9 0 0 0 0 1 0 | 0 3 9 0 3 0 0 0 0 0 0 0 0 | 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 | * * * * 280 * * * * * * * * * * * * * | 0 0 1 0 0 0 0 1 xo.. .... oo..3oo..3ox.. ....&#x & ♦ 2 4 | 1 8 0 6 0 | 0 4 12 0 0 0 4 0 0 | 0 0 6 8 0 0 0 0 0 1 0 0 0 | 0 0 0 4 0 2 0 0 0 0 0 0 0 0 0 0 | * * * * * 210 * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 .... oo..3oo..3oo..3ox.. ....&#x & ♦ 1 5 | 0 5 0 10 0 | 0 0 10 0 0 0 10 0 0 | 0 0 0 10 0 0 0 0 0 5 0 0 0 | 0 0 0 0 0 5 0 0 0 0 0 0 1 0 0 0 | * * * * * * 84 * * * * * * * * * * * | 0 1 0 0 0 0 1 0 .... o.x.3o.o.3o.o.3o.o. ....&#x & ♦ 1 5 | 0 0 5 10 0 | 0 0 0 0 10 0 10 0 0 | 0 0 0 0 0 10 0 0 0 5 0 0 0 | 0 0 0 0 0 0 5 0 0 0 0 0 1 0 0 0 | * * * * * * * 84 * * * * * * * * * * | 0 0 0 1 0 0 1 0 xoo. .... .... ooo.3oxo. ....&#x & ♦ 2 4 | 1 6 2 3 3 | 0 3 6 1 0 6 1 0 3 | 0 0 3 2 0 0 3 0 6 0 0 1 0 | 0 0 0 1 0 0 0 3 0 0 2 0 0 0 0 0 | * * * * * * * * 840 * * * * * * * * * | 0 0 0 0 1 0 0 1 xoo. .... .... .... oxo.3ooo.&#x & ♦ 2 4 | 1 6 2 3 3 | 0 3 6 1 0 6 0 1 3 | 0 0 3 0 2 0 3 0 6 0 1 0 0 | 0 0 0 0 1 0 0 3 0 0 0 2 0 0 0 0 | * * * * * * * * * 420 * * * * * * * * | 0 0 0 0 0 0 0 2 .... oox.3ooo.3ooo. .... ....&#x & ♦ 1 5 | 0 1 4 6 4 | 0 0 0 0 6 4 4 0 6 | 0 0 0 0 0 4 0 6 0 1 0 4 0 | 0 0 0 0 0 0 1 0 4 0 0 0 0 0 1 0 | * * * * * * * * * * 210 * * * * * * * | 0 0 0 0 0 0 2 0 .... oox.3ooo. .... oxo. ....&#x & ♦ 1 5 | 0 2 3 4 6 | 0 0 1 0 3 6 1 0 9 | 0 0 0 0 0 1 0 6 3 0 0 2 3 | 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0 1 | * * * * * * * * * * * 840 * * * * * * | 0 0 0 0 0 1 1 0 .... oox. .... ooo.3oxo. ....&#x & ♦ 1 5 | 0 3 2 4 6 | 0 0 3 0 1 6 1 0 9 | 0 0 0 1 0 0 0 3 6 0 0 2 3 | 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 1 | * * * * * * * * * * * * 840 * * * * * | 0 0 0 0 0 0 1 1 .... oox. .... .... oxo.3ooo.&#x & ♦ 1 5 | 0 3 2 4 6 | 0 0 3 0 1 6 0 1 9 | 0 0 0 0 1 0 0 3 6 0 2 0 3 | 0 0 0 0 0 0 0 0 0 3 0 2 0 1 0 0 | * * * * * * * * * * * * * 840 * * * * | 0 0 0 0 0 1 0 1 .... .... ooo.3ooo.3oxo. ....&#x & ♦ 1 5 | 0 4 1 6 4 | 0 0 6 0 0 4 4 0 6 | 0 0 0 4 0 0 0 0 6 1 0 4 0 | 0 0 0 0 0 1 0 0 0 0 4 0 0 0 1 0 | * * * * * * * * * * * * * * 420 * * * | 0 0 0 0 1 0 1 0 .o..3.o..3.o..3.o..3.x.. .... & ♦ 0 6 | 0 0 0 15 0 | 0 0 0 0 0 0 20 0 0 | 0 0 0 0 0 0 0 0 0 15 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 | * * * * * * * * * * * * * * * 14 * * | 0 1 0 1 0 0 0 0 .oo.3.ox. .... .oo.3.xo. ....&#x & ♦ 0 6 | 0 0 0 6 9 | 0 0 0 0 0 0 1 1 18 | 0 0 0 0 0 0 0 0 0 0 3 3 9 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 | * * * * * * * * * * * * * * * * 280 * | 0 0 0 0 0 1 0 1 .oo.3.ox. .... .... .xo.3.oo.&#x ♦ 0 6 | 0 0 0 6 9 | 0 0 0 0 0 0 0 2 18 | 0 0 0 0 0 0 0 0 0 0 6 0 9 | 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 | * * * * * * * * * * * * * * * * * 140 | 0 0 0 0 0 0 0 2 ------------------------------------+-------+-------------------+-----------------------------------+--------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------------+------------------------- x...3o...3o...3o...3o...3o... & ♦ 7 0 | 21 0 0 0 0 | 35 0 0 0 0 0 0 0 0 | 35 0 0 0 0 0 0 0 0 0 0 0 0 | 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * xo..3oo..3oo..3oo..3ox.. ....&#x & ♦ 6 6 | 15 30 0 15 0 | 20 60 60 0 0 0 20 0 0 | 15 60 90 60 0 0 0 0 0 15 0 0 0 | 6 30 60 60 0 30 0 0 0 0 0 0 6 0 0 0 | 1 6 15 20 0 15 6 0 0 0 0 0 0 0 0 1 0 0 | * 14 * * * * * * xo..3oo..3oo.. .... ox..3oo..&#x & ♦ 4 3 | 6 12 0 3 0 | 4 18 12 0 0 0 0 1 0 | 1 12 18 0 4 0 0 0 0 0 0 0 0 | 0 3 12 0 6 0 0 0 0 0 0 0 0 0 0 0 | 0 0 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 70 * * * * * .... o.x.3o.o.3o.o.3o.o.3o.o.&#x & ♦ 1 6 | 0 0 6 15 0 | 0 0 0 0 15 0 20 0 0 | 0 0 0 0 0 20 0 0 0 15 0 0 0 | 0 0 0 0 0 0 15 0 0 0 0 0 6 0 0 0 | 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 1 0 0 | * * * 14 * * * * xoo. .... ooo.3ooo.3oxo. ....&#x & ♦ 2 5 | 1 8 2 6 4 | 0 4 12 1 0 8 4 0 6 | 0 0 6 8 0 0 4 0 12 1 0 4 0 | 0 0 0 4 0 2 0 6 0 0 8 0 0 0 1 0 | 0 0 0 0 0 1 0 0 4 0 0 0 0 0 2 0 0 0 | * * * * 210 * * * .... oox.3ooo. .... oxo.3ooo.&#x & ♦ 1 6 | 0 3 3 6 9 | 0 0 3 0 3 9 1 1 18 | 0 0 0 0 1 1 0 9 9 0 3 3 9 | 0 0 0 0 0 0 0 0 3 9 0 3 0 3 0 3 | 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 1 0 | * * * * * 280 * * .... ooox3oooo3oooo3oxoo ....&#xr ♦ 2 10 | 0 10 10 20 20 | 0 0 20 0 20 40 20 0 60 | 0 0 0 20 0 20 0 60 60 10 0 40 30 | 0 0 0 0 0 10 10 0 40 60 40 0 2 0 10 20 | 0 0 0 0 0 0 2 2 0 0 10 20 20 0 10 0 0 0 | * * * * * * 42 * xoo.3oox. .... ooo.3oxo.3ooo.&#xt & ♦ 3 9 | 3 18 6 15 18 | 1 18 36 3 3 36 4 5 54 | 0 6 36 12 12 0 18 18 72 0 18 12 36 | 0 0 12 12 12 0 0 36 0 36 24 24 0 24 0 12 | 0 0 0 4 4 0 0 0 12 12 0 0 12 12 0 0 4 4 | * * * * * * * 70
oo3xo3oo3oo3oo3ox3oo&#zx → height = 0 (tegum sum of 2 mutually inverted rocs) o.3o.3o.3o.3o.3o.3o. & | 56 ♦ 12 15 | 6 30 180 | 40 80 240 360 | 30 300 150 600 | 12 240 60 36 180 120 | 2 12 70 15 ---------------------------+----+---------+--------------+--------------------+--------------------+----------------------------+------------- .. x. .. .. .. .. .. & | 2 | 336 * ♦ 1 5 10 | 10 10 30 30 | 10 40 30 80 | 5 40 10 10 35 20 | 1 5 15 5 oo3oo3oo3oo3oo3oo3oo&#x | 2 | * 420 ♦ 0 0 16 | 0 8 24 48 | 0 48 16 96 | 0 48 12 4 32 24 | 0 4 16 6 ---------------------------+----+---------+--------------+--------------------+--------------------+----------------------------+------------- o.3x. .. .. .. .. .. & | 3 | 3 0 | 112 * * ♦ 0 10 0 0 | 0 30 0 0 | 0 20 10 0 0 0 | 0 0 5 5 .. x.3o. .. .. .. .. & | 3 | 3 0 | * 560 * ♦ 4 0 6 0 | 6 0 12 12 | 4 4 0 6 12 4 | 1 4 4 1 .. xo .. .. .. .. ..&#x & | 3 | 1 2 | * * 3360 ♦ 0 1 3 6 | 0 9 3 18 | 0 12 3 1 8 6 | 0 2 5 3 ---------------------------+----+---------+--------------+--------------------+--------------------+----------------------------+------------- .. x.3o.3o. .. .. .. & ♦ 4 | 6 0 | 0 4 0 | 560 * * * ♦ 3 0 3 0 | 3 0 0 3 3 0 | 1 3 1 0 oo3xo .. .. .. .. ..&#x & ♦ 4 | 3 3 | 1 0 3 | * 1120 * * ♦ 0 6 0 0 | 0 6 3 0 0 0 | 0 0 2 3 .. xo3oo .. .. .. ..&#x & ♦ 4 | 3 3 | 0 1 3 | * * 3360 * ♦ 0 0 2 4 | 0 2 0 1 4 2 | 0 2 2 1 .. xo .. .. .. ox ..&#x ♦ 4 | 2 4 | 0 0 4 | * * * 5040 ♦ 0 2 0 4 | 0 4 1 0 2 2 | 0 1 2 2 ---------------------------+----+---------+--------------+--------------------+--------------------+----------------------------+------------- .. x.3o.3o.3o. .. .. & ♦ 5 | 10 0 | 0 10 0 | 5 0 0 0 | 336 * * * | 2 0 0 1 0 0 | 1 2 0 0 oo3xo .. .. .. ox ..&#x & ♦ 5 | 4 6 | 1 0 9 | 0 2 0 3 | * 3360 * * | 0 2 1 0 0 0 | 0 0 1 2 .. xo3oo3oo .. .. ..&#x & ♦ 5 | 6 4 | 0 4 6 | 1 0 4 0 | * * 1680 * | 0 0 0 1 2 0 | 0 2 1 0 .. xo3oo .. .. ox ..&#x & ♦ 5 | 4 6 | 0 1 9 | 0 0 2 3 | * * * 6720 | 0 1 0 0 1 1 | 0 1 1 1 ---------------------------+----+---------+--------------+--------------------+--------------------+----------------------------+------------- .. x.3o.3o.3o.3o. .. & ♦ 6 | 15 0 | 0 20 0 | 15 0 0 0 | 6 0 0 0 | 112 * * * * * | 1 1 0 0 oo3xo .. .. oo3ox ..&#x & ♦ 6 | 6 9 | 1 1 18 | 0 3 3 9 | 0 3 0 3 | * 2240 * * * * | 0 0 1 1 oo3xo .. .. .. ox3oo&#x ♦ 6 | 6 9 | 2 0 18 | 0 6 0 9 | 0 6 0 0 | * * 560 * * * | 0 0 0 2 .. xo3oo3oo3oo .. ..&#x & ♦ 6 | 10 5 | 0 10 10 | 5 0 10 0 | 1 0 5 0 | * * * 336 * * | 0 2 0 0 .. xo3oo3oo .. ox ..&#x & ♦ 6 | 7 8 | 0 4 16 | 1 0 8 6 | 0 0 2 4 | * * * * 1680 * | 0 1 1 0 .. xo3oo .. oo3ox ..&#x ♦ 6 | 6 9 | 0 2 18 | 0 0 6 9 | 0 0 0 6 | * * * * * 1120 | 0 1 0 1 ---------------------------+----+---------+--------------+--------------------+--------------------+----------------------------+------------- .. x.3o.3o.3o.3o.3o. & ♦ 7 | 21 0 | 0 35 0 | 35 0 0 0 | 21 0 0 0 | 7 0 0 0 0 0 | 16 * * * .. xo3oo3oo3oo3ox ..&#x ♦ 12 | 30 30 | 0 40 120 | 30 0 120 90 | 12 0 60 120 | 2 0 0 12 30 20 | * 56 * * oo3xo .. oo3oo3ox ..&#x & ♦ 7 | 9 12 | 1 4 30 | 1 4 12 18 | 0 6 3 12 | 0 4 0 0 3 0 | * * 560 * oo3xo3oo .. oo3ox3oo&#zx ♦ 12 | 24 36 | 8 8 144 | 0 48 48 144 | 0 96 0 96 | 0 32 16 0 0 16 | * * * 70
ox xo3oo3oo *c3oo3oo3ox&#zx → height = 0 (tegum sum of hax and geep) o. o.3o.3o. *c3o.3o.3o. | 32 * ♦ 15 12 0 0 | 60 6 120 30 0 | 20 60 60 360 180 40 0 | 30 180 120 240 360 120 30 0 | 6 60 120 120 60 120 120 30 12 0 0 | 15 30 40 12 2 0 .o .o3.o3.o *c3.o3.o3.o | * 24 ♦ 0 16 1 10 | 0 16 80 80 40 | 0 0 80 160 240 160 80 | 0 160 40 80 320 240 160 80 | 0 40 80 80 16 80 160 80 80 16 16 | 10 16 40 16 16 1 ----------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- .. x. .. .. .. .. .. | 2 0 | 240 * * * ♦ 8 0 8 0 0 | 4 12 4 48 12 0 0 | 8 24 24 48 48 8 0 0 | 2 12 24 24 16 24 16 2 0 0 0 | 6 8 8 4 0 0 oo oo3oo3oo *c3oo3oo3oo&#x | 1 1 | * 384 * * ♦ 0 1 10 5 0 | 0 0 10 30 30 10 0 | 0 30 10 20 60 30 10 0 | 0 10 20 20 5 20 30 10 5 0 0 | 5 5 10 5 1 0 .x .. .. .. .. .. .. | 0 2 | * * 12 * ♦ 0 16 0 0 0 | 0 0 80 0 0 0 0 | 0 160 0 0 0 0 0 0 | 0 40 80 0 0 0 0 0 0 0 0 | 10 16 0 0 0 0 .. .. .. .. .. .. .x | 0 2 | * * * 120 ♦ 0 0 0 8 8 | 0 0 0 0 24 32 24 | 0 0 0 0 32 48 48 32 | 0 0 0 8 0 8 32 24 32 8 8 | 1 0 8 8 8 1 ----------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- .. x.3o. .. .. .. .. | 3 0 | 3 0 0 0 | 640 * * * * ♦ 1 3 0 6 0 0 0 | 3 3 6 12 6 0 0 0 | 1 3 6 6 6 6 2 0 0 0 0 | 3 3 2 2 0 0 ox .. .. .. .. .. ..&#x | 1 2 | 0 2 1 0 | * 192 * * * ♦ 0 0 10 0 0 0 0 | 0 30 0 0 0 0 0 0 | 0 10 20 0 0 0 0 0 0 0 0 | 5 5 0 0 0 0 .. xo .. .. .. .. ..&#x | 2 1 | 1 2 0 0 | * * 1920 * * ♦ 0 0 1 6 3 0 0 | 0 6 3 6 12 3 0 0 | 0 3 6 6 2 6 6 1 0 0 0 | 3 2 3 2 0 0 .. .. .. .. .. .. ox&#x | 1 2 | 0 2 0 1 | * * * 960 * ♦ 0 0 0 0 6 4 0 | 0 0 0 0 12 12 6 0 | 0 0 0 4 0 4 12 6 4 0 0 | 1 0 4 4 1 0 .. .. .. .. .. .o3.x | 0 3 | 0 0 0 3 | * * * * 320 ♦ 0 0 0 0 0 4 6 | 0 0 0 0 0 6 12 12 | 0 0 0 0 0 0 4 6 12 4 4 | 0 0 1 4 4 1 ----------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- .. x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | 160 * * * * * * ♦ 0 0 6 0 0 0 0 0 | 0 3 0 6 0 0 0 0 0 0 0 | 3 0 2 0 0 0 .. x.3o. .. *c3o. .. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | * 480 * * * * * ♦ 2 0 0 4 0 0 0 0 | 1 0 2 0 4 2 0 0 0 0 0 | 1 2 0 2 0 0 ox xo .. .. .. .. ..&#x ♦ 2 2 | 1 4 1 0 | 0 2 2 0 0 | * * 960 * * * * ♦ 0 6 0 0 0 0 0 0 | 0 3 6 0 0 0 0 0 0 0 0 | 3 2 0 0 0 0 .. xo3oo .. .. .. ..&#x ♦ 3 1 | 3 3 0 0 | 1 0 3 0 0 | * * * 3840 * * * ♦ 0 1 1 2 2 0 0 0 | 0 1 2 2 1 2 1 0 0 0 0 | 2 1 1 1 0 0 .. xo .. .. .. .. ox&#x ♦ 2 2 | 1 4 0 1 | 0 0 2 2 0 | * * * * 2880 * * ♦ 0 0 0 0 4 2 0 0 | 0 0 0 2 0 2 4 1 0 0 0 | 1 0 2 2 0 0 .. .. .. .. .. oo3ox&#x ♦ 1 3 | 0 3 0 3 | 0 0 0 3 1 | * * * * * 1280 * ♦ 0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 3 3 3 0 0 | 0 0 1 3 1 0 .. .. .. .. .o3.o3.x ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * * 480 ♦ 0 0 0 0 0 0 2 4 | 0 0 0 0 0 0 0 1 4 2 2 | 0 0 0 2 2 1 ----------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- .. x.3o. .. *c3o.3o. .. ♦ 5 0 | 10 0 0 0 | 10 0 0 0 0 | 0 5 0 0 0 0 0 | 192 * * * * * * * | 1 0 0 0 2 0 0 0 0 0 0 | 0 1 0 2 0 0 ox xo3oo .. .. .. ..&#x ♦ 3 2 | 3 6 1 0 | 1 3 6 0 0 | 0 0 3 2 0 0 0 | * 1920 * * * * * * | 0 1 2 0 0 0 0 0 0 0 0 | 2 1 0 0 0 0 .. xo3oo3oo .. .. ..&#x ♦ 4 1 | 6 4 0 0 | 4 0 6 0 0 | 1 0 0 4 0 0 0 | * * 960 * * * * * | 0 1 0 2 0 0 0 0 0 0 0 | 2 0 1 0 0 0 .. xo3oo .. *c3oo .. ..&#x ♦ 4 1 | 6 4 0 0 | 4 0 6 0 0 | 0 1 0 4 0 0 0 | * * * 1920 * * * * | 0 0 1 0 1 1 0 0 0 0 0 | 1 1 0 1 0 0 .. xo3oo .. .. .. ox&#x ♦ 3 2 | 3 6 0 1 | 1 0 6 3 0 | 0 0 0 2 3 0 0 | * * * * 3840 * * * | 0 0 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0 0 .. xo .. .. .. oo3ox&#x ♦ 2 3 | 1 6 0 3 | 0 0 3 6 1 | 0 0 0 0 3 2 0 | * * * * * 1920 * * | 0 0 0 0 0 0 2 1 0 0 0 | 0 0 1 2 0 0 .. .. .. .. oo3oo3ox&#x ♦ 1 4 | 0 4 0 6 | 0 0 0 6 4 | 0 0 0 0 0 4 1 | * * * * * * 960 * | 0 0 0 0 0 0 0 1 2 0 0 | 0 0 0 2 1 0 .. .. .o .. *c3.o3.o3.x ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * * 384 | 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1 ----------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- .. x.3o. .. *c3o.3o.3o. ♦ 6 0 | 15 0 0 0 | 20 0 0 0 0 | 0 15 0 0 0 0 0 | 6 0 0 0 0 0 0 0 | 32 * * * * * * * * * * | 0 0 0 2 0 0 ox xo3oo3oo .. .. ..&#x ♦ 4 2 | 6 8 1 0 | 4 4 12 0 0 | 1 0 6 8 0 0 0 | 0 4 2 0 0 0 0 0 | * 480 * * * * * * * * * | 2 0 0 0 0 0 ox xo3oo .. *c3oo .. ..&#x ♦ 4 2 | 6 8 1 0 | 4 4 12 0 0 | 0 1 6 8 0 0 0 | 0 4 0 2 0 0 0 0 | * * 960 * * * * * * * * | 1 1 0 0 0 0 .. xo3oo3oo .. .. ox&#x ♦ 4 2 | 6 8 0 1 | 4 0 12 4 0 | 1 0 0 8 6 0 0 | 0 0 2 0 4 0 0 0 | * * * 960 * * * * * * * | 1 0 1 0 0 0 .. xo3oo .. *c3oo3oo ..&#x ♦ 5 1 | 10 5 0 0 | 10 0 10 0 0 | 0 5 0 10 0 0 0 | 1 0 0 5 0 0 0 0 | * * * * 384 * * * * * * | 0 1 0 1 0 0 .. xo3oo .. *c3oo .. ox&#x ♦ 4 2 | 6 8 0 1 | 4 0 12 4 0 | 0 1 0 8 6 0 0 | 0 0 0 2 4 0 0 0 | * * * * * 960 * * * * * | 1 0 0 1 0 0 .. xo3oo .. .. oo3ox&#x ♦ 3 3 | 3 9 0 3 | 1 0 9 9 1 | 0 0 0 3 9 3 0 | 0 0 0 0 3 3 0 0 | * * * * * * 1280 * * * * | 0 0 1 1 0 0 .. xo .. .. oo3oo3ox&#x ♦ 2 4 | 1 8 0 6 | 0 0 4 12 4 | 0 0 0 0 6 8 1 | 0 0 0 0 0 4 2 0 | * * * * * * * 480 * * * | 0 0 0 2 0 0 .. .. oo .. *c3oo3oo3ox&#x ♦ 1 5 | 0 5 0 10 | 0 0 0 10 10 | 0 0 0 0 0 10 5 | 0 0 0 0 0 0 5 1 | * * * * * * * * 384 * * | 0 0 0 1 1 0 .. .o3.o .. *c3.o3.o3.x ♦ 0 6 | 0 0 0 15 | 0 0 0 0 20 | 0 0 0 0 0 0 15 | 0 0 0 0 0 0 0 6 | * * * * * * * * * 64 * | 0 0 0 1 0 1 .. .. .o3.o *c3.o3.o3.x ♦ 0 6 | 0 0 0 15 | 0 0 0 0 20 | 0 0 0 0 0 0 15 | 0 0 0 0 0 0 0 6 | * * * * * * * * * * 64 | 0 0 0 0 1 1 ----------------------------+-------+----------------+----------------------+--------------------------------+-------------------------------------+-------------------------------------------+------------------- ox xo3oo3oo *c3oo .. ox&#zx ♦ 8 4 | 24 32 2 2 | 32 16 96 16 0 | 8 8 48 128 48 0 0 | 0 64 32 32 64 0 0 0 | 0 16 16 16 0 16 0 0 0 0 0 | 60 * * * * * ox xo3oo .. *c3oo3oo ..&#x ♦ 5 2 | 10 10 1 0 | 10 5 20 0 0 | 0 5 10 20 0 0 0 | 1 10 0 10 0 0 0 0 | 0 0 5 0 2 0 0 0 0 0 0 | * 192 * * * * .. xo3oo3oo .. oo3ox&#x ♦ 4 3 | 6 12 0 3 | 4 0 18 12 1 | 1 0 0 12 18 4 0 | 0 0 3 0 12 6 0 0 | 0 0 0 3 0 0 4 0 0 0 0 | * * 320 * * * .. xo3oo .. *c3oo3oo3ox&#x ♦ 6 6 | 15 30 0 15 | 20 0 60 60 20 | 0 15 0 60 90 60 15 | 6 0 0 30 60 60 30 6 | 1 0 0 0 6 15 20 15 6 1 0 | * * * 64 * * .. .. oo3oo *c3oo3oo3ox&#x ♦ 1 6 | 0 6 0 15 | 0 0 0 15 20 | 0 0 0 0 0 20 15 | 0 0 0 0 0 0 15 6 | 0 0 0 0 0 0 0 0 6 0 1 | * * * * 64 * .. .o3.o3.o *c3.o3.o3.x ♦ 0 12 | 0 0 0 60 | 0 0 0 0 160 | 0 0 0 0 0 0 240 | 0 0 0 0 0 0 0 192 | 0 0 0 0 0 0 0 0 0 32 32 | * * * * * 2
xxoo xoxo xoox oxoo3oooo3ooxo *e3ooox&#zx → all heights = 0 (tegum sum of 3 mutually gyrated, lacings-orthogonal hexips and a cube within lacings subspace only) o... o... o... o...3o...3o... *e3o... | 8 * ♦ 3 24 0 0 0 | 48 72 96 0 0 0 0 | 144 96 96 288 96 0 0 0 0 0 0 0 | 192 48 288 192 72 288 0 0 0 0 0 0 | 48 48 192 72 48 96 144 0 0 0 0 0 0 | 3 24 48 24 0 0 .o.. .o.. .o.. .o..3.o..3.o.. *e3.o.. & | * 48 ♦ 0 4 1 6 16 | 4 24 32 12 24 72 48 | 24 48 16 144 48 8 8 48 64 24 96 192 | 48 32 72 128 48 192 40 20 60 240 80 120 | 16 16 64 24 40 80 120 12 12 72 96 72 24 | 1 20 20 24 6 28 --------------------------------------------+------+-------------------+------------------------------+--------------------------------------------------+------------------------------------------------------+----------------------------------------------------+-------------------- x... .... .... .... .... .... .... & | 2 0 | 12 * * * * ♦ 16 0 0 0 0 0 0 | 48 0 32 0 0 0 0 0 0 0 0 0 | 64 0 96 0 0 0 0 0 0 0 0 0 | 16 16 64 24 0 0 0 0 0 0 0 0 0 | 2 8 16 0 0 0 oo.. oo.. oo.. oo..3oo..3oo.. *e3oo..&#x & | 1 1 | * 192 * * * ♦ 2 6 8 0 0 0 0 | 12 12 8 36 12 0 0 0 0 0 0 0 | 24 8 36 32 12 48 0 0 0 0 0 0 | 8 8 32 12 10 20 30 0 0 0 0 0 0 | 1 9 10 6 0 0 .x.. .... .... .... .... .... .... & | 0 2 | * * 24 * * ♦ 0 0 0 0 16 0 0 | 0 0 0 0 0 0 8 24 0 0 48 0 | 0 0 0 0 0 0 16 0 48 96 0 0 | 0 0 0 0 0 0 0 4 12 48 32 24 0 | 0 4 0 0 6 16 .... .... .... .x.. .... .... .... & | 0 2 | * * * 144 * ♦ 0 4 0 4 0 8 0 | 4 16 0 16 0 4 0 4 16 4 0 16 | 16 16 8 32 8 16 8 8 0 16 16 16 | 8 8 16 4 16 16 16 4 0 4 16 8 4 | 1 8 8 4 1 4 .oo. .oo. .oo. .oo.3.oo.3.oo. *e3.oo.&#x & | 0 2 | * * * * 384 ♦ 0 0 2 0 2 6 6 | 0 0 1 12 6 0 1 6 6 3 15 30 | 0 0 6 12 6 30 6 2 12 48 14 24 | 0 0 6 3 4 14 24 2 3 18 22 18 6 | 0 7 2 6 3 8 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