vertex figure of rag,
equatorial cross-section of hex-first hax
- related segmentotera:
- octpyp squascop
- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices Hanner polytopes
links
| Acronym | hexip |
| Name |
hexadecachoron prism, vertex figure of rag, equatorial cross-section of hex-first hax |
| Circumradius | sqrt(3)/2 = 0.866025 |
| Coordinates | (1/sqrt(2), 0, 0, 0, 1/2) & all permutations in all but last coord., all changes of sign |
| Volume | 1/6 = 0.166667 |
| Face vector | 16, 56, 88, 64, 18 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x x3o3o4o . . . . . | 16 | 1 6 | 6 12 | 12 8 | 8 1 ----------+----+------+-------+-------+----- x . . . . | 2 | 8 * ♦ 6 0 | 12 0 | 8 0 . x . . . | 2 | * 48 | 1 4 | 4 4 | 4 1 ----------+----+------+-------+-------+----- x x . . . | 4 | 2 2 | 24 * | 4 0 | 4 0 . x3o . . | 3 | 0 3 | * 64 | 1 2 | 2 1 ----------+----+------+-------+-------+----- x x3o . . ♦ 6 | 3 6 | 3 2 | 32 * | 2 0 . x3o3o . ♦ 4 | 0 6 | 0 4 | * 32 | 1 1 ----------+----+------+-------+-------+----- x x3o3o . ♦ 8 | 4 12 | 6 8 | 4 2 | 16 * . x3o3o4o ♦ 8 | 0 24 | 0 32 | 0 16 | * 2
x x3o3o *c3o . . . . . | 16 | 1 6 | 6 12 | 12 4 4 | 4 4 1 -------------+----+------+-------+----------+------ x . . . . | 2 | 8 * ♦ 6 0 | 12 0 0 | 4 4 0 . x . . . | 2 | * 48 | 1 4 | 4 2 2 | 2 2 1 -------------+----+------+-------+----------+------ x x . . . | 4 | 2 2 | 24 * | 4 0 0 | 2 2 0 . x3o . . | 3 | 0 3 | * 64 | 1 1 1 | 1 1 1 -------------+----+------+-------+----------+------ x x3o . . ♦ 6 | 3 6 | 3 2 | 32 * * | 1 1 0 . x3o3o . ♦ 4 | 0 6 | 0 4 | * 16 * | 1 0 1 . x3o . *c3o ♦ 4 | 0 6 | 0 4 | * * 16 | 0 1 1 -------------+----+------+-------+----------+------ x x3o3o . ♦ 8 | 4 12 | 6 8 | 4 1 0 | 8 * * x x3o . *c3o ♦ 8 | 4 12 | 6 8 | 4 0 1 | * 8 * . x3o3o *c3o ♦ 8 | 0 24 | 0 32 | 0 8 8 | * * 2
x s2o3o4s
. demi( . . . . ) | 16 | 1 3 3 | 3 3 9 3 | 3 1 9 3 4 | 3 1 1 4
------------------+----+---------+-------------+--------------+--------
x demi( . . . . ) | 2 | 8 * * ♦ 3 3 0 0 | 0 0 9 3 0 | 3 1 0 4
. s 2 . s | 2 | * 24 * | 1 0 4 0 | 2 0 4 0 2 | 2 0 1 2
. . . o4s | 2 | * * 24 | 0 1 2 2 | 1 1 2 2 2 | 1 1 1 2
------------------+----+---------+-------------+--------------+--------
x s 2 . s | 4 | 2 2 0 | 12 * * * | 0 0 4 0 0 | 2 0 0 2
x . . o4s | 4 | 2 0 2 | * 12 * * | 0 0 2 2 0 | 1 1 0 2
. sefa( s 2 o4s ) | 3 | 0 2 1 | * * 48 * | 1 0 1 0 1 | 1 0 1 1
. sefa( . o3o4s ) | 3 | 0 0 3 | * * * 16 | 0 1 0 1 1 | 0 1 1 1
------------------+----+---------+-------------+--------------+--------
. s 2 o4s ♦ 4 | 0 4 2 | 0 0 4 0 | 12 * * * * | 1 0 1 0
. . o3o4s ♦ 4 | 0 0 6 | 0 0 0 4 | * 4 * * * | 0 1 1 0
x sefa( s 2 o4s ) ♦ 6 | 3 4 2 | 2 1 2 0 | * * 24 * * | 1 0 0 1
x sefa( . o3o4s ) ♦ 6 | 3 0 6 | 0 3 0 2 | * * * 8 * | 0 1 0 1
. sefa( s2o3o4s ) ♦ 4 | 0 3 3 | 0 0 3 1 | * * * * 16 | 0 0 1 1
------------------+----+---------+-------------+--------------+--------
x s 2 o4s ♦ 8 | 4 8 4 | 4 2 8 0 | 2 0 4 0 0 | 6 * * *
x . o3o4s ♦ 8 | 4 0 12 | 0 6 0 8 | 0 2 0 4 0 | * 2 * *
s2o3o4s ♦ 8 | 0 12 12 | 0 0 24 8 | 6 2 0 0 8 | * * 2 *
x sefa( s2o3o4s ) ♦ 8 | 4 6 6 | 3 3 6 2 | 0 0 3 1 2 | * * * 8
starting figure: x x o3o4x
xx3oo3oo4oo&#x → height = 1
(hex || hex)
o.3o.3o.4o. | 8 * | 6 1 0 | 12 6 0 | 8 12 0 | 1 8 0
.o3.o3.o4.o | * 8 | 0 1 6 | 0 6 12 | 0 12 8 | 0 8 1
---------------+-----+---------+----------+----------+-------
x. .. .. .. | 2 0 | 24 * * | 4 1 0 | 4 4 0 | 1 4 0
oo3oo3oo4oo&#x | 1 1 | * 8 * ♦ 0 6 0 | 0 12 0 | 0 8 0
.x .. .. .. | 0 2 | * * 24 | 0 1 4 | 0 4 4 | 0 4 1
---------------+-----+---------+----------+----------+-------
x.3o. .. .. | 3 0 | 3 0 0 | 32 * * | 2 1 0 | 1 2 0
xx .. .. ..&#x | 2 2 | 1 2 1 | * 24 * | 0 4 0 | 0 4 0
.x3.o .. .. | 0 3 | 0 0 3 | * * 32 | 0 1 2 | 0 2 1
---------------+-----+---------+----------+----------+-------
x.3o.3o. .. ♦ 4 0 | 6 0 0 | 4 0 0 | 16 * * | 1 1 0
xx3oo .. ..&#x ♦ 3 3 | 3 3 3 | 1 3 1 | * 32 * | 0 2 0
.x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * 16 | 0 1 1
---------------+-----+---------+----------+----------+-------
x.3o.3o.4o. ♦ 8 0 | 24 0 0 | 32 0 0 | 16 0 0 | 1 * *
xx3oo3oo ..&#x ♦ 4 4 | 6 4 6 | 4 6 4 | 1 4 1 | * 16 *
.x3.o3.o4.o ♦ 0 8 | 0 0 24 | 0 0 32 | 0 0 16 | * * 1
xx3oo3oo *b3oo&#x → height = 1
(hex || hex)
o.3o.3o. *b3o. | 8 * | 6 1 0 | 12 6 0 | 4 4 12 0 0 | 1 4 4 0
.o3.o3.o *b3.o | * 8 | 0 1 6 | 0 6 12 | 0 0 12 4 4 | 0 4 4 1
------------------+-----+---------+----------+------------+--------
x. .. .. .. | 2 0 | 24 * * | 4 1 0 | 2 2 4 0 0 | 1 2 2 0
oo3oo3oo *b3oo&#x | 1 1 | * 8 * ♦ 0 6 0 | 0 0 12 0 0 | 0 4 4 0
.x .. .. .. | 0 2 | * * 24 | 0 1 4 | 0 0 4 2 2 | 0 2 2 1
------------------+-----+---------+----------+------------+--------
x.3o. .. .. | 3 0 | 3 0 0 | 32 * * | 1 1 1 0 0 | 1 1 1 0
xx .. .. ..&#x | 2 2 | 1 2 1 | * 24 * | 0 0 4 0 0 | 0 2 2 0
.x3.o .. .. | 0 3 | 0 0 3 | * * 32 | 0 0 1 1 1 | 0 1 1 1
------------------+-----+---------+----------+------------+--------
x.3o.3o. .. ♦ 4 0 | 6 0 0 | 4 0 0 | 8 * * * * | 1 1 0 0
x.3o. .. *b3o. ♦ 4 0 | 6 0 0 | 4 0 0 | * 8 * * * | 1 0 1 0
xx3oo .. ..&#x ♦ 3 3 | 3 3 3 | 1 3 1 | * * 32 * * | 0 1 1 0
.x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * * 8 * | 0 1 0 1
.x3.o .. *b3.x ♦ 0 4 | 0 0 6 | 0 0 4 | * * * * 8 | 0 0 1 1
------------------+-----+---------+----------+------------+--------
x.3o.3o. *b3o. ♦ 8 0 | 24 0 0 | 32 0 0 | 8 8 0 0 0 | 1 * * *
xx3oo3oo ..&#x ♦ 4 4 | 6 4 6 | 4 6 4 | 1 0 4 1 0 | * 8 * *
xx3oo .. *b3oo&#x ♦ 4 4 | 6 4 6 | 4 6 4 | 0 1 4 0 1 | * * 8 *
.x3.o3.o *b3.o ♦ 0 8 | 0 0 24 | 0 0 32 | 0 0 0 8 8 | * * * 1
xoox3oooo3oxxo&#xr → height(1,2) = height(3,4) = 1/sqrt(2) = 0.707107
height(2,3) = height(4,1) = 1
(tet || (tet || dual tet) || dual tet)
o...3o...3o... | 4 * * * | 3 3 1 0 0 0 0 0 | 3 6 3 3 3 0 0 0 0 0 0 | 1 3 3 1 3 6 3 0 0 0 0 0 0 0 | 1 1 3 3 1 0 0
.o..3.o..3.o.. | * 4 * * | 0 3 0 3 1 0 0 0 | 0 3 6 0 3 3 3 0 0 0 0 | 0 1 3 3 0 3 6 1 3 0 0 0 0 0 | 1 0 1 3 3 1 0
..o.3..o.3..o. | * * 4 * | 0 0 1 0 0 3 3 0 | 0 0 0 3 3 0 0 3 6 3 0 | 0 0 0 0 3 6 3 0 0 1 3 3 1 0 | 0 1 3 3 1 0 1
...o3...o3...o | * * * 4 | 0 0 0 0 1 0 3 3 | 0 0 0 0 3 0 3 0 3 6 3 | 0 0 0 0 0 3 6 0 3 0 1 3 3 1 | 0 0 1 3 3 1 1
-------------------+---------+-------------------+----------------------------+-------------------------------+--------------
x... .... .... | 2 0 0 0 | 6 * * * * * * * | 2 2 0 1 0 0 0 0 0 0 0 | 1 2 1 0 2 2 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0
oo..3oo..3oo..&#x | 1 1 0 0 | * 12 * * * * * * | 0 2 2 0 1 0 0 0 0 0 0 | 0 1 2 1 0 2 2 0 0 0 0 0 0 0 | 1 0 1 2 1 0 0
o.o.3o.o.3o.o.&#x | 1 0 1 0 | * * 4 * * * * * ♦ 0 0 0 3 3 0 0 0 0 0 0 | 0 0 0 0 3 6 3 0 0 0 0 0 0 0 | 0 1 3 3 1 0 0
.... .... .x.. | 0 2 0 0 | * * * 6 * * * * | 0 0 2 0 0 2 1 0 0 0 0 | 0 0 1 2 0 0 2 1 2 0 0 0 0 0 | 1 0 0 1 2 1 0
.o.o3.o.o3.o.o&#x | 0 1 0 1 | * * * * 4 * * * ♦ 0 0 0 0 3 0 3 0 0 0 0 | 0 0 0 0 0 3 6 0 3 0 0 0 0 0 | 0 0 1 3 3 1 0
..x. .... .... | 0 0 2 0 | * * * * * 6 * * | 0 0 0 1 0 0 0 2 2 0 0 | 0 0 0 0 2 2 0 0 0 1 2 1 0 0 | 0 1 2 1 0 0 1
..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * 12 * | 0 0 0 0 1 0 0 0 2 2 0 | 0 0 0 0 0 2 2 0 0 0 1 2 1 0 | 0 0 1 2 1 0 1
.... .... ...x | 0 0 0 2 | * * * * * * * 6 | 0 0 0 0 0 0 1 0 0 2 2 | 0 0 0 0 0 0 2 0 2 0 0 1 2 1 | 0 0 0 1 2 1 1
-------------------+---------+-------------------+----------------------------+-------------------------------+--------------
x...3o... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0
xo.. .... ....&#x | 2 1 0 0 | 1 2 0 0 0 0 0 0 | * 12 * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0
.... .... ox..&#x | 1 2 0 0 | 0 2 0 1 0 0 0 0 | * * 12 * * * * * * * * | 0 0 1 1 0 0 1 0 0 0 0 0 0 0 | 1 0 0 1 1 0 0
x.x. .... ....&#x | 2 0 2 0 | 1 0 2 0 0 1 0 0 | * * * 6 * * * * * * * | 0 0 0 0 2 2 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0 0
oooo3oooo3oooo&#xr | 1 1 1 1 | 0 1 1 0 1 0 1 0 | * * * * 12 * * * * * * | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 | 0 0 1 2 1 0 0
.... .o..3.x.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 | * * * * * 4 * * * * * | 0 0 0 1 0 0 0 1 1 0 0 0 0 0 | 1 0 0 0 1 1 0
.... .... .x.x&#x | 0 2 0 2 | 0 0 0 1 2 0 0 1 | * * * * * * 6 * * * * | 0 0 0 0 0 0 2 0 2 0 0 0 0 0 | 0 0 0 1 2 1 0
..x.3..o. .... | 0 0 3 0 | 0 0 0 0 0 3 0 0 | * * * * * * * 4 * * * | 0 0 0 0 1 0 0 0 0 1 1 0 0 0 | 0 1 1 0 0 0 1
..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * 12 * * | 0 0 0 0 0 1 0 0 0 0 1 1 0 0 | 0 0 1 1 0 0 1
.... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * * 12 * | 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 0 1 1 0 1
.... ...o3...x | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 0 1 1 1
-------------------+---------+-------------------+----------------------------+-------------------------------+--------------
x...3o...3o... ♦ 4 0 0 0 | 6 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 1 0 0 0 0 0
xo..3oo.. ....&#x ♦ 3 1 0 0 | 3 3 0 0 0 0 0 0 | 1 3 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * | 1 0 1 0 0 0 0
xo.. .... ox..&#x ♦ 2 2 0 0 | 1 4 0 1 0 0 0 0 | 0 2 2 0 0 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * | 1 0 0 1 0 0 0
.... oo..3ox..&#x ♦ 1 3 0 0 | 0 3 0 3 0 0 0 0 | 0 0 3 0 0 1 0 0 0 0 0 | * * * 4 * * * * * * * * * * | 1 0 0 0 1 0 0
x.x.3o.o. ....&#x ♦ 3 0 3 0 | 3 0 3 0 0 3 0 0 | 1 0 0 3 0 0 0 1 0 0 0 | * * * * 4 * * * * * * * * * | 0 1 1 0 0 0 0
xoox .... ....&#xr ♦ 2 1 2 1 | 1 2 2 0 1 1 2 0 | 0 1 0 1 2 0 0 0 1 0 0 | * * * * * 12 * * * * * * * * | 0 0 1 1 0 0 0
.... .... oxxo&#xr ♦ 1 2 1 2 | 0 2 1 1 2 0 2 1 | 0 0 1 0 2 0 1 0 0 1 0 | * * * * * * 12 * * * * * * * | 0 0 0 1 1 0 0
.o..3.o..3.x.. ♦ 0 4 0 0 | 0 0 0 6 0 0 0 0 | 0 0 0 0 0 4 0 0 0 0 0 | * * * * * * * 1 * * * * * * | 1 0 0 0 0 1 0
.... .o.o3.x.x&#x ♦ 0 3 0 3 | 0 0 0 3 3 0 0 3 | 0 0 0 0 0 1 3 0 0 0 1 | * * * * * * * * 4 * * * * * | 0 0 0 0 1 1 0
..x.3..o.3..o. ♦ 0 0 4 0 | 0 0 0 0 0 6 0 0 | 0 0 0 0 0 0 0 4 0 0 0 | * * * * * * * * * 1 * * * * | 0 1 0 0 0 0 1
..xo3..oo ....&#x ♦ 0 0 3 1 | 0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 0 1 3 0 0 | * * * * * * * * * * 4 * * * | 0 0 1 0 0 0 1
..xo .... ..ox&#x ♦ 0 0 2 2 | 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * 6 * * | 0 0 0 1 0 0 1
.... ..oo3..ox&#x ♦ 0 0 1 3 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * * * 4 * | 0 0 0 0 1 0 1
...o3...o3...x ♦ 0 0 0 4 | 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * 1 | 0 0 0 0 0 1 1
-------------------+---------+-------------------+----------------------------+-------------------------------+--------------
xo..3oo..3ox..&#x ♦ 4 4 0 0 | 6 12 0 6 0 0 0 0 | 4 12 12 0 0 4 0 0 0 0 0 | 1 4 6 4 0 0 0 1 0 0 0 0 0 0 | 1 * * * * * *
x.x.3o.o.3o.o.&#x ♦ 4 0 4 0 | 6 0 4 0 0 6 0 0 | 4 0 0 6 0 0 0 4 0 0 0 | 1 0 0 0 4 0 0 0 0 1 0 0 0 0 | * 1 * * * * *
xoox3oooo ....&#xr ♦ 3 1 3 1 | 3 3 3 0 1 3 3 0 | 1 3 0 3 3 0 0 1 3 0 0 | 0 1 0 0 1 3 0 0 0 0 1 0 0 0 | * * 4 * * * *
xoox .... oxxo&#xr ♦ 2 2 2 2 | 1 4 2 1 2 1 4 1 | 0 2 2 1 4 0 1 0 2 2 0 | 0 0 1 0 0 2 2 0 0 0 0 1 0 0 | * * * 6 * * *
.... oooo3oxxo&#xr ♦ 1 3 1 3 | 0 3 1 3 3 0 3 3 | 0 0 3 0 3 1 3 0 0 3 1 | 0 0 0 1 0 0 3 0 1 0 0 0 1 0 | * * * * 4 * *
.o.o3.o.o3.x.x&#x ♦ 0 4 0 4 | 0 0 0 6 4 0 0 6 | 0 0 0 0 0 4 6 0 0 0 4 | 0 0 0 0 0 0 0 1 4 0 0 0 0 1 | * * * * * 1 *
..xo3..oo3..ox&#x ♦ 0 0 4 4 | 0 0 0 0 0 6 12 6 | 0 0 0 0 0 0 0 4 12 12 4 | 0 0 0 0 0 0 0 0 0 1 4 6 4 1 | * * * * * * 1
or o...3o...3o... & | 8 * | 3 3 1 0 | 3 6 3 3 3 0 | 1 3 3 1 3 6 0 | 1 1 4 3 .o..3.o..3.o.. & | * 8 | 0 3 1 3 | 0 3 6 3 3 3 | 0 1 3 3 3 6 1 | 1 1 4 3 ---------------------+-----+------------+-----------------+-----------------+-------- x... .... .... & | 2 0 | 12 * * * | 2 2 0 1 0 0 | 1 2 1 0 2 2 0 | 1 1 2 1 oo..3oo..3oo..&#x & | 1 1 | * 24 * * | 0 2 2 0 1 0 | 0 1 2 1 0 4 0 | 1 0 2 2 o.o.3o.o.3o.o.&#x & | 1 1 | * * 8 * ♦ 0 0 0 3 3 0 | 0 0 0 0 3 9 0 | 0 1 4 3 .... .... .x.. & | 0 2 | * * * 12 | 0 0 2 1 0 2 | 0 0 1 2 2 2 1 | 1 1 2 1 ---------------------+-----+------------+-----------------+-----------------+-------- x...3o... .... & | 3 0 | 3 0 0 0 | 8 * * * * * | 1 1 0 0 1 0 0 | 1 1 1 0 xo.. .... ....&#x & | 2 1 | 1 2 0 0 | * 24 * * * * | 0 1 1 0 0 1 0 | 1 0 1 1 .... .... ox..&#x & | 1 2 | 0 2 0 1 | * * 24 * * * | 0 0 1 1 0 1 0 | 1 0 1 1 x.x. .... ....&#x & | 2 2 | 1 0 2 1 | * * * 12 * * | 0 0 0 0 2 2 0 | 0 1 2 1 oooo3oooo3oooo&#xr | 2 2 | 0 2 2 0 | * * * * 12 * | 0 0 0 0 0 4 0 | 0 0 2 2 .... .o..3.x.. & | 0 3 | 0 0 0 3 | * * * * * 8 | 0 0 0 1 1 0 1 | 1 1 1 0 ---------------------+-----+------------+-----------------+-----------------+-------- x...3o...3o... & ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 | 2 * * * * * * | 1 1 0 0 xo..3oo.. ....&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 | * 8 * * * * * | 1 0 1 0 xo.. .... ox..&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 0 | * * 12 * * * * | 1 0 0 1 .... oo..3ox..&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * * 8 * * * | 1 0 1 0 x.x.3o.o. ....&#x & ♦ 3 3 | 3 0 3 3 | 1 0 0 3 0 1 | * * * * 8 * * | 0 1 1 0 xoox .... ....&#xr & ♦ 3 3 | 1 4 3 1 | 0 1 1 1 2 0 | * * * * * 24 * | 0 0 1 1 .o..3.o..3.x.. & ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 4 | * * * * * * 2 | 1 1 0 0 ---------------------+-----+------------+-----------------+-----------------+-------- xo..3oo..3ox..&#x & ♦ 4 4 | 6 12 0 6 | 4 12 12 0 0 4 | 1 4 6 4 0 0 1 | 2 * * * x.x.3o.o.3o.o.&#x & ♦ 4 4 | 6 0 4 6 | 4 0 0 6 0 4 | 1 0 0 0 4 0 1 | * 2 * * xoox3oooo ....&#xr & ♦ 4 4 | 3 6 4 3 | 1 3 3 3 3 1 | 0 1 0 1 1 3 0 | * * 8 * xoox .... oxxo&#xr ♦ 4 4 | 2 8 4 2 | 0 4 4 2 4 0 | 0 0 2 0 0 4 0 | * * * 6
xxx oxo3ooo4ooo&#xt → both heights = 1/sqrt(2) = 0.707107 (line || pseudo ope || line) o.. o..3o..4o.. | 2 * * | 1 6 0 0 0 0 | 6 12 0 0 0 0 | 12 8 0 0 0 | 8 1 0 .o. .o.3.o.4.o. | * 12 * | 0 1 1 4 1 0 | 1 4 4 4 1 4 | 4 4 4 4 4 | 4 1 4 ..o ..o3..o4..o | * * 2 | 0 0 0 0 6 1 | 0 0 0 0 6 12 | 0 0 0 12 8 | 0 1 8 --------------------+--------+----------------+-----------------+---------------+------ x.. ... ... ... | 2 0 0 | 1 * * * * * ♦ 6 0 0 0 0 0 | 12 0 0 0 0 | 8 0 0 oo. oo.3oo.4oo.&#x | 1 1 0 | * 12 * * * * | 1 4 0 0 0 0 | 4 4 0 0 0 | 4 1 0 .x. ... ... ... | 0 2 0 | * * 6 * * * ♦ 1 0 4 0 1 0 | 4 0 4 4 0 | 4 0 4 ... .x. ... ... | 0 2 0 | * * * 24 * * | 0 1 1 2 0 1 | 1 2 2 1 2 | 2 1 2 .oo .oo3.oo4.oo&#x | 0 1 1 | * * * * 12 * | 0 0 0 0 1 4 | 0 0 0 4 4 | 0 1 4 ..x ... ... ... | 0 0 2 | * * * * * 1 ♦ 0 0 0 0 6 0 | 0 0 0 12 0 | 0 0 8 --------------------+--------+----------------+-----------------+---------------+------ xx. ... ... ...&#x | 2 2 0 | 1 2 1 0 0 0 | 6 * * * * * | 4 0 0 0 0 | 4 0 0 ... ox. ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 24 * * * * | 1 2 0 0 0 | 2 1 0 .x. .x. ... ... | 0 4 0 | 0 0 2 2 0 0 | * * 12 * * * | 1 0 2 1 0 | 2 0 2 ... .x.3.o. ... | 0 3 0 | 0 0 0 3 0 0 | * * * 16 * * | 0 1 1 0 1 | 1 1 1 .xx ... ... ...&#x | 0 2 2 | 0 0 1 0 2 1 | * * * * 6 * | 0 0 0 4 0 | 0 0 4 ... .xo ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * 24 | 0 0 0 1 2 | 0 1 2 --------------------+--------+----------------+-----------------+---------------+------ xx. ox. ... ...&#x ♦ 2 4 0 | 1 4 2 2 0 0 | 2 2 1 0 0 0 | 12 * * * * | 2 0 0 ... ox.3oo. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 1 0 0 | * 16 * * * | 1 1 0 .x. .x.3.o. ... ♦ 0 6 0 | 0 0 3 6 0 0 | 0 0 3 2 0 0 | * * 8 * * | 1 0 1 .xx .xo ... ...&#x ♦ 0 4 2 | 0 0 2 2 4 1 | 0 0 1 0 2 2 | * * * 12 * | 0 0 2 ... .xo3.oo ...&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 1 0 3 | * * * * 16 | 0 1 1 --------------------+--------+----------------+-----------------+---------------+------ xx. ox.3oo. ...&#x ♦ 2 6 0 | 1 6 3 6 0 0 | 3 6 3 2 0 0 | 3 2 1 0 0 | 8 * * ... oxo3ooo4ooo&#xt ♦ 1 6 1 | 0 6 0 12 6 0 | 0 12 0 8 0 12 | 0 8 0 0 8 | * 2 * .xx .xo3.oo ...&#x ♦ 0 6 2 | 0 0 3 6 6 1 | 0 0 3 2 3 6 | 0 0 1 3 2 | * * 8
xx xo3oo3ox&#x → height = 1/sqrt(2) = 0.707107
(tepe || inv tepe)
o. o.3o.3o. | 8 * | 1 3 3 0 0 | 3 3 3 6 3 0 0 | 3 1 6 3 3 3 1 0 0 | 1 3 3 1 1 0
.o .o3.o3.o | * 8 | 0 0 3 1 3 | 0 0 3 3 6 3 3 | 0 0 3 6 1 3 3 3 1 | 0 1 3 3 1 1
---------------+-----+--------------+------------------+----------------------+------------
x. .. .. .. | 2 0 | 4 * * * * ♦ 3 0 3 0 0 0 0 | 3 0 6 3 0 0 0 0 0 | 1 3 3 1 0 0
.. x. .. .. | 2 0 | * 12 * * * | 1 2 0 2 0 0 0 | 2 1 2 0 2 1 0 0 0 | 1 2 1 0 1 0
oo oo3oo3oo&#x | 1 1 | * * 24 * * | 0 0 1 2 1 0 0 | 0 0 2 2 1 2 1 0 0 | 0 1 2 1 1 0
.x .. .. .. | 0 2 | * * * 4 * ♦ 0 0 3 0 0 3 0 | 0 0 3 6 0 0 0 3 0 | 0 1 3 3 0 1
.. .. .. .x | 0 2 | * * * * 12 | 0 0 0 0 2 1 2 | 0 0 0 2 0 1 2 2 1 | 0 0 1 2 1 1
---------------+-----+--------------+------------------+----------------------+------------
x. x. .. .. | 4 0 | 2 2 0 0 0 | 6 * * * * * * | 2 0 2 0 0 0 0 0 0 | 1 2 1 0 0 0
.. x.3o. .. | 3 0 | 0 3 0 0 0 | * 8 * * * * * | 1 1 0 0 1 0 0 0 0 | 1 1 0 0 1 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * 12 * * * * | 0 0 2 2 0 0 0 0 0 | 0 1 2 1 0 0
.. xo .. ..&#x | 2 1 | 0 1 2 0 0 | * * * 24 * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 0 1 0
.. .. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * 24 * * | 0 0 0 1 0 1 1 0 0 | 0 0 1 1 1 0
.x .. .. .x | 0 4 | 0 0 0 2 2 | * * * * * 6 * | 0 0 0 2 0 0 0 2 0 | 0 0 1 2 0 1
.. .. .o3.x | 0 3 | 0 0 0 0 3 | * * * * * * 8 | 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1
---------------+-----+--------------+------------------+----------------------+------------
x. x.3o. .. ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 0 | 4 * * * * * * * * | 1 1 0 0 0 0
.. x.3o.3o. ♦ 4 0 | 0 6 0 0 0 | 0 4 0 0 0 0 0 | * 2 * * * * * * * | 1 0 0 0 1 0
xx xo .. ..&#x ♦ 4 2 | 2 2 4 1 0 | 1 0 2 2 0 0 0 | * * 12 * * * * * * | 0 1 1 0 0 0
xx .. .. ox&#x ♦ 2 4 | 1 0 4 2 2 | 0 0 2 0 2 1 0 | * * * 12 * * * * * | 0 0 1 1 0 0
.. xo3oo ..&#x ♦ 3 1 | 0 3 3 0 0 | 0 1 0 3 0 0 0 | * * * * 8 * * * * | 0 1 0 0 1 0
.. xo .. ox&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 0 2 2 0 0 | * * * * * 12 * * * | 0 0 1 0 1 0
.. .. oo3ox&#x ♦ 1 3 | 0 0 3 0 3 | 0 0 0 0 3 0 1 | * * * * * * 8 * * | 0 0 0 1 1 0
.x .. .o3.x ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * * 4 * | 0 0 0 1 0 1
.. .o3.o3.x | 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * * * 2 | 0 0 0 0 1 1
---------------+-----+--------------+------------------+----------------------+------------
x. x.3o.3o. ♦ 8 0 | 4 12 0 0 0 | 6 8 0 0 0 0 0 | 4 2 0 0 0 0 0 0 0 | 1 * * * * *
xx xo3oo ..&#x ♦ 6 2 | 3 6 6 1 0 | 3 2 3 6 0 0 0 | 1 0 3 0 2 0 0 0 0 | * 4 * * * *
xx xo .. ox&#x ♦ 4 4 | 2 2 8 2 2 | 1 0 4 4 4 1 0 | 0 0 2 2 0 2 0 0 0 | * * 6 * * *
xx .. oo3ox&#x ♦ 2 6 | 1 0 6 3 6 | 0 0 3 0 6 3 2 | 0 0 0 3 0 0 2 1 0 | * * * 4 * *
.. xo3oo3ox&#x ♦ 4 4 | 0 6 12 0 6 | 0 4 0 12 12 0 4 | 0 1 0 0 4 6 4 0 1 | * * * * 2 *
.x .o3.o3.x ♦ 0 8 | 0 0 0 4 12 | 0 0 0 0 0 6 8 | 0 0 0 0 0 0 0 4 2 | * * * * * 1
xx xo4oo ox4oo&#zx → height = 0 (tegum sum of 2 base-orthogonal cubes) o. o.4o. o.4o. | 8 * | 1 2 4 0 0 | 2 4 8 4 0 | 8 4 8 | 8 1 .o .o4.o .o4.o | * 8 | 0 0 4 1 2 | 0 4 4 8 2 | 4 8 8 | 8 1 -------------------+-----+------------+--------------+----------+----- x. .. .. .. .. | 2 0 | 4 * * * * ♦ 2 4 0 0 0 | 8 4 0 | 8 0 .. x. .. .. .. | 2 0 | * 8 * * * | 1 0 4 0 0 | 4 0 4 | 4 1 oo oo4oo oo4oo&#x | 1 1 | * * 32 * * | 0 1 2 2 0 | 2 2 4 | 4 1 .x .. .. .. .. | 0 2 | * * * 4 * ♦ 0 4 0 0 2 | 4 8 0 | 8 0 .. .. .. .x .. | 0 2 | * * * * 8 | 0 0 0 4 1 | 0 4 4 | 4 1 -------------------+-----+------------+--------------+----------+----- x. x. .. .. .. | 4 0 | 2 2 0 0 0 | 4 * * * * | 4 0 0 | 4 0 xx .. .. .. ..&#x | 2 2 | 1 0 2 1 0 | * 16 * * * | 2 2 0 | 4 0 .. xo .. .. ..&#x | 2 1 | 0 1 2 0 0 | * * 32 * * | 1 0 2 | 2 1 .. .. .. ox ..&#x | 1 2 | 0 0 2 0 1 | * * * 32 * | 0 1 2 | 2 1 .x .. .. .x .. | 0 4 | 0 0 0 2 2 | * * * * 4 | 0 4 0 | 4 0 -------------------+-----+------------+--------------+----------+----- xx xo .. .. ..&#x ♦ 4 2 | 2 2 4 1 0 | 1 2 2 0 0 | 16 * * | 2 0 xx .. .. ox ..&#x ♦ 2 4 | 1 0 4 2 2 | 0 2 0 2 1 | * 16 * | 2 0 .. xo .. ox ..&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 2 2 0 | * * 32 | 1 1 -------------------+-----+------------+--------------+----------+----- xx xo .. ox ..&#x ♦ 4 4 | 2 2 8 2 2 | 1 4 4 4 1 | 2 2 2 | 16 * .. xo4oo ox4oo&#zx ♦ 4 4 | 0 4 16 0 4 | 0 0 16 16 0 | 0 0 16 | * 2
xx xo xo ox ox&#zx → height = 0 (tegum sum of 2 base-orthogonal cubes) o. o. o. o. o. | 8 * | 1 1 1 4 0 0 0 | 1 1 4 4 4 2 2 0 0 | 4 4 2 2 2 2 2 2 | 2 2 2 2 1 .o .o .o .o .o | * 8 | 0 0 0 4 1 1 1 | 0 0 4 2 2 4 4 1 1 | 2 2 4 4 2 2 2 2 | 2 2 2 2 1 -------------------+-----+----------------+------------------------+-----------------+---------- x. .. .. .. .. | 2 0 | 4 * * * * * * ♦ 1 1 4 0 0 0 0 0 0 | 4 4 2 2 0 0 0 0 | 2 2 2 2 0 .. x. .. .. .. | 2 0 | * 4 * * * * * | 1 0 0 4 0 0 0 0 0 | 4 0 0 0 2 2 0 0 | 2 2 0 0 1 .. .. x. .. .. | 2 0 | * * 4 * * * * | 0 1 0 0 4 0 0 0 0 | 0 4 0 0 0 0 2 2 | 0 0 2 2 1 oo oo4oo oo4oo&#x | 1 1 | * * * 32 * * * | 0 0 1 1 1 1 1 0 0 | 1 1 1 1 1 1 1 1 | 1 1 1 1 1 .x .. .. .. .. | 0 2 | * * * * 4 * * ♦ 0 0 4 0 0 0 0 1 1 | 2 2 4 4 0 0 0 0 | 2 2 2 2 0 .. .. .. .x .. | 0 2 | * * * * * 4 * | 0 0 0 0 0 4 0 1 0 | 0 0 4 0 2 0 2 0 | 2 0 2 0 1 .. .. .. .. .x | 0 2 | * * * * * * 4 | 0 0 0 0 0 0 4 0 1 | 0 0 0 4 0 2 0 2 | 0 2 0 2 1 -------------------+-----+----------------+------------------------+-----------------+---------- x. x. .. .. .. | 4 0 | 2 2 0 0 0 0 0 | 2 * * * * * * * * | 4 0 0 0 0 0 0 0 | 2 2 0 0 0 x. .. x. .. .. | 4 0 | 2 0 2 0 0 0 0 | * 2 * * * * * * * | 0 4 0 0 0 0 0 0 | 0 0 2 2 0 xx .. .. .. ..&#x | 2 2 | 1 0 0 2 1 0 0 | * * 16 * * * * * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 0 .. xo .. .. ..&#x | 2 1 | 0 1 0 2 0 0 0 | * * * 16 * * * * * | 1 0 0 0 1 1 0 0 | 1 1 0 0 1 .. .. xo .. ..&#x | 2 1 | 0 0 1 2 0 0 0 | * * * * 16 * * * * | 0 1 0 0 0 0 1 1 | 0 0 1 1 1 .. .. .. ox ..&#x | 1 2 | 0 0 0 2 0 1 0 | * * * * * 16 * * * | 0 0 1 0 1 0 1 0 | 1 0 1 0 1 .. .. .. .. ox&#x | 1 2 | 0 0 0 2 0 0 1 | * * * * * * 16 * * | 0 0 0 1 0 1 0 1 | 0 1 0 1 1 .x .. .. .x .. | 0 4 | 0 0 0 0 2 2 0 | * * * * * * * 2 * | 0 0 4 0 0 0 0 0 | 2 0 2 0 0 .x .. .. .. .x | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * * 2 | 0 0 0 4 0 0 0 0 | 0 2 0 2 0 -------------------+-----+----------------+------------------------+-----------------+---------- xx xo .. .. ..&#x ♦ 4 2 | 2 2 0 4 1 0 0 | 1 0 2 2 0 0 0 0 0 | 8 * * * * * * * | 1 1 0 0 0 xx .. xo .. ..&#x ♦ 4 2 | 2 0 2 4 1 0 0 | 0 1 2 0 2 0 0 0 0 | * 8 * * * * * * | 0 0 1 1 0 xx .. .. ox ..&#x ♦ 2 4 | 1 0 0 4 2 2 0 | 0 0 2 0 0 2 0 1 0 | * * 8 * * * * * | 1 0 1 0 0 xx .. .. .. ox&#x ♦ 2 4 | 1 0 0 4 2 0 2 | 0 0 2 0 0 0 2 0 1 | * * * 8 * * * * | 0 1 0 1 0 .. xo .. ox ..&#x ♦ 2 2 | 0 1 0 4 0 1 0 | 0 0 0 2 0 2 0 0 0 | * * * * 8 * * * | 1 0 0 0 1 .. xo .. .. ox&#x ♦ 2 2 | 0 1 0 4 0 0 1 | 0 0 0 2 0 0 2 0 0 | * * * * * 8 * * | 0 1 0 0 1 .. .. xo ox ..&#x ♦ 2 2 | 0 0 1 4 0 1 0 | 0 0 0 0 2 2 0 0 0 | * * * * * * 8 * | 0 0 1 0 1 .. .. xo .. ox&#x ♦ 2 2 | 0 0 1 4 0 0 1 | 0 0 0 0 2 0 2 0 0 | * * * * * * * 8 | 0 0 0 1 1 -------------------+-----+----------------+------------------------+-----------------+---------- xx xo .. ox ..&#x ♦ 4 4 | 2 2 0 8 2 2 0 | 1 0 4 4 0 4 0 1 0 | 2 0 2 0 2 0 0 0 | 4 * * * * xx xo .. .. ox&#x ♦ 4 4 | 2 2 0 8 2 0 2 | 1 0 4 4 0 0 4 0 1 | 2 0 0 2 0 2 0 0 | * 4 * * * xx .. xo ox ..&#x ♦ 4 4 | 2 0 2 8 2 2 0 | 0 1 4 0 4 4 0 1 0 | 0 2 2 0 0 0 2 0 | * * 4 * * xx .. xo .. ox&#x ♦ 4 4 | 2 0 2 8 2 0 2 | 0 1 4 0 4 0 4 0 1 | 0 2 0 2 0 0 0 2 | * * * 4 * .. xo xo ox ox&#zx ♦ 4 4 | 0 2 2 16 0 2 2 | 0 0 0 8 8 8 8 0 0 | 0 0 0 0 4 4 4 4 | * * * * 2
xoxo oxox xxxx&#xr → all cyclical heights = 1/sqrt(2) = 0.707107
(in fact this lace simplex degenerates into a square)
o... o... o... | 4 * * * | 1 1 2 1 2 0 0 0 0 0 0 0 0 0 | 1 2 1 2 1 2 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 1 2 1 1 2 2 2 1 2 2 0 0 0 0 0 0 0 0 | 1 1 1 2 1 1 2 0 0 0
.o.. .o.. .o.. | * 4 * * | 0 0 2 0 0 1 1 2 1 0 0 0 0 0 | 0 1 2 2 0 0 0 0 2 2 0 1 1 2 2 1 2 0 0 0 0 0 | 1 1 2 0 0 0 2 2 1 2 0 0 2 1 1 2 1 2 0 0 0 | 1 0 2 1 0 1 2 1 1 0
..o. ..o. ..o. | * * 4 * | 0 0 0 1 0 0 0 2 0 1 1 2 0 0 | 0 0 0 0 1 0 0 0 2 0 2 0 2 1 2 0 2 1 2 1 2 0 | 0 0 0 0 0 0 1 2 0 0 1 2 2 1 2 1 2 2 1 2 1 | 0 0 1 0 1 1 2 1 2 1
...o ...o ...o | * * * 4 | 0 0 0 0 2 0 0 0 1 0 0 2 1 1 | 0 0 0 0 0 1 2 2 0 2 2 0 0 0 0 1 2 0 1 2 2 1 | 0 0 0 1 1 2 0 0 1 2 2 2 2 0 0 0 1 2 1 1 2 | 0 1 0 1 2 1 2 0 1 1
-------------------+---------+-----------------------------+---------------------------------------------+-------------------------------------------+--------------------
x... .... .... | 2 0 0 0 | 2 * * * * * * * * * * * * * | 1 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 0 1 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 2 0 1 0 0 0 0
.... .... x... | 2 0 0 0 | * 2 * * * * * * * * * * * * ♦ 1 0 0 2 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 2 1 0 2 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 | 1 1 1 2 1 0 2 0 0 0
oo.. oo.. oo..&#x | 1 1 0 0 | * * 8 * * * * * * * * * * * | 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 1 1 0 0 0
o.o. o.o. o.o.&#x | 1 0 1 0 | * * * 4 * * * * * * * * * * | 0 0 0 0 1 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 2 0 0 1 2 2 0 0 0 0 0 0 0 0 | 0 0 1 0 1 1 2 0 0 0
o..o o..o o..o&#x | 1 0 0 1 | * * * * 8 * * * * * * * * * | 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 | 0 1 0 1 1 1 1 0 0 0
.... .x.. .... | 0 2 0 0 | * * * * * 2 * * * * * * * * | 0 0 2 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 | 1 0 2 0 0 0 2 0 0 0 0 0 0 1 0 2 0 0 0 0 0 | 1 0 2 0 0 1 0 1 0 0
.... .... .x.. | 0 2 0 0 | * * * * * * 2 * * * * * * * ♦ 0 0 0 2 0 0 0 0 0 0 0 1 0 0 2 1 0 0 0 0 0 0 | 0 1 2 0 0 0 0 2 0 2 0 0 0 0 1 2 0 2 0 0 0 | 1 0 2 1 0 0 2 1 1 0
.oo. .oo. .oo.&#x | 0 1 1 0 | * * * * * * * 8 * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 | 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 | 0 0 1 0 0 1 1 1 1 0
.o.o .o.o .o.o&#x | 0 1 0 1 | * * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 2 0 0 2 0 0 0 1 2 0 0 0 | 0 0 0 1 0 1 2 0 1 0
..x. .... .... | 0 0 2 0 | * * * * * * * * * 2 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 2 0 1 2 0 | 0 0 0 0 0 1 0 1 2 1
.... .... ..x. | 0 0 2 0 | * * * * * * * * * * 2 * * * ♦ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 2 0 | 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 1 0 2 0 2 1 | 0 0 1 0 1 0 2 1 2 1
..oo ..oo ..oo&#x | 0 0 1 1 | * * * * * * * * * * * 8 * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 | 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 | 0 0 0 0 1 1 1 0 1 1
.... ...x .... | 0 0 0 2 | * * * * * * * * * * * * 2 * | 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 | 0 0 0 1 0 2 0 0 0 0 2 0 0 0 0 0 0 0 1 0 2 | 0 1 0 0 2 1 0 0 0 1
.... .... ...x | 0 0 0 2 | * * * * * * * * * * * * * 2 ♦ 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 2 1 | 0 0 0 0 1 2 0 0 0 2 0 2 0 0 0 0 0 2 0 1 2 | 0 1 0 1 2 0 2 0 1 1
-------------------+---------+-----------------------------+---------------------------------------------+-------------------------------------------+--------------------
x... .... x... | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 2 0 0 0 0 0 0
xo.. .... ....&#x | 2 1 0 0 | 1 0 2 0 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 1 0 1 0 0 0 0
.... ox.. ....&#x | 1 2 0 0 | 0 0 2 0 0 1 0 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 0 0 1 0 0 0 0
.... .... xx..&#x | 2 2 0 0 | 0 1 2 0 0 0 1 0 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 1 0 0 0
.... .... x.x.&#x | 2 0 2 0 | 0 1 0 2 0 0 0 0 0 0 1 0 0 0 | * * * * 2 * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 0 2 0 0 0
x..o .... ....&#x | 2 0 0 1 | 1 0 0 0 2 0 0 0 0 0 0 0 0 0 | * * * * * 4 * * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 0 1 0 0 0 0
.... o..x ....&#x | 1 0 0 2 | 0 0 0 0 2 0 0 0 0 0 0 0 1 0 | * * * * * * 4 * * * * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 1 1 0 0 0 0
.... .... x..x&#x | 2 0 0 2 | 0 1 0 0 2 0 0 0 0 0 0 0 0 1 | * * * * * * * 4 * * * * * * * * * * * * * * | 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 | 0 1 0 1 1 0 1 0 0 0
ooo. ooo. ooo.&#x | 1 1 1 0 | 0 0 1 1 0 0 0 1 0 0 0 0 0 0 | * * * * * * * * 8 * * * * * * * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 | 0 0 1 0 0 1 1 0 0 0
oo.o oo.o oo.o&#x | 1 1 0 1 | 0 0 1 0 1 0 0 0 1 0 0 0 0 0 | * * * * * * * * * 8 * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 0 0 0 1 0 1 1 0 0 0
o.oo o.oo o.oo&#x | 1 0 1 1 | 0 0 0 1 1 0 0 0 0 0 0 1 0 0 | * * * * * * * * * * 8 * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 0 0 0
.... .x.. .x.. | 0 4 0 0 | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 | * * * * * * * * * * * 1 * * * * * * * * * * | 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 | 1 0 2 0 0 0 0 1 0 0
.ox. .... ....&#x | 0 1 2 0 | 0 0 0 0 0 0 0 2 0 1 0 0 0 0 | * * * * * * * * * * * * 4 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 | 0 0 0 0 0 1 0 1 1 0
.... .xo. ....&#x | 0 2 1 0 | 0 0 0 0 0 1 0 2 0 0 0 0 0 0 | * * * * * * * * * * * * * 4 * * * * * * * * | 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 | 0 0 1 0 0 1 0 1 0 0
.... .... .xx.&#x | 0 2 2 0 | 0 0 0 0 0 0 1 2 0 0 1 0 0 0 | * * * * * * * * * * * * * * 4 * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 | 0 0 1 0 0 0 1 1 1 0
.... .... .x.x&#x | 0 2 0 2 | 0 0 0 0 0 0 1 0 2 0 0 0 0 1 | * * * * * * * * * * * * * * * 2 * * * * * * | 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 | 0 0 0 1 0 0 2 0 1 0
.ooo .ooo .ooo&#x | 0 1 1 1 | 0 0 0 0 0 0 0 1 1 0 0 1 0 0 | * * * * * * * * * * * * * * * * 8 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 | 0 0 0 0 0 1 1 0 1 0
..x. .... ..x. | 0 0 4 0 | 0 0 0 0 0 0 0 0 0 2 2 0 0 0 | * * * * * * * * * * * * * * * * * 1 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 | 0 0 0 0 0 0 0 1 2 1
..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 0 0 0 0 1 0 2 0 0 | * * * * * * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 | 0 0 0 0 0 1 0 0 1 1
.... ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 | 0 0 0 0 1 1 0 0 0 1
.... .... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 | 0 0 0 0 1 0 1 0 1 1
.... ...x ....x | 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 | 0 1 0 0 2 0 0 0 0 1
-------------------+---------+-----------------------------+---------------------------------------------+-------------------------------------------+--------------------
xo.. ox.. ....&#x ♦ 2 2 0 0 | 1 0 4 0 0 1 0 0 0 0 0 0 0 0 | 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 1 0 0 0 0
xo.. .... xx..&#x ♦ 4 2 0 0 | 2 2 4 0 0 0 1 0 0 0 0 0 0 0 | 1 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 0
.... ox.. xx..&#x ♦ 2 4 0 0 | 0 1 4 0 0 2 2 0 0 0 0 0 0 0 | 0 0 2 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0
x..o o..x ....&#x ♦ 2 0 0 2 | 1 0 0 0 4 0 0 0 0 0 0 0 1 0 | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 2 * * * * * * * * * * * * * * * * * | 0 1 0 0 0 1 0 0 0 0
x..o .... x..x&#x ♦ 4 0 0 2 | 2 2 0 0 4 0 0 0 0 0 0 0 0 1 | 1 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 2 * * * * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0
.... o..x x..x&#x ♦ 2 0 0 4 | 0 1 0 0 4 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | * * * * * 2 * * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0
.... oxo. ....&#x ♦ 1 2 1 0 | 0 0 2 1 0 1 0 2 0 0 0 0 0 0 | 0 0 1 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * 4 * * * * * * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0
.... .... xxx.&#x ♦ 2 2 2 0 | 0 1 2 2 0 0 1 2 0 0 1 0 0 0 | 0 0 0 1 1 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * * * * * * * | 0 0 1 0 0 0 1 0 0 0
xo.o .... ....&#x ♦ 2 1 0 1 | 1 0 2 0 2 0 0 0 1 0 0 0 0 0 | 0 1 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 4 * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0
.... .... xx.x&#x ♦ 2 2 0 2 | 0 1 2 0 2 0 1 0 2 0 0 0 0 1 | 0 0 0 1 0 0 0 1 0 2 0 0 0 0 0 1 0 0 0 0 0 0 | * * * * * * * * * 4 * * * * * * * * * * * | 0 0 0 1 0 0 1 0 0 0
.... o.ox ....&#x ♦ 1 0 1 2 | 0 0 0 1 2 0 0 0 0 0 0 2 1 0 | 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 | * * * * * * * * * * 4 * * * * * * * * * * | 0 0 0 0 1 1 0 0 0 0
.... .... x.xx&#x ♦ 2 0 2 2 | 0 1 0 2 2 0 0 0 0 0 1 2 0 1 | 0 0 0 0 1 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 1 0 | * * * * * * * * * * * 4 * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0
oooo oooo oooo&#x ♦ 1 1 1 1 | 0 0 1 1 1 0 0 1 1 0 0 1 0 0 | 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 | * * * * * * * * * * * * 8 * * * * * * * * | 0 0 0 0 0 1 1 0 0 0
.ox. .xo. ....&#x ♦ 0 2 2 0 | 0 0 0 0 0 1 0 4 0 1 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * 2 * * * * * * * | 0 0 0 0 0 1 0 1 0 0
.ox. .... .xx.&#x ♦ 0 2 4 0 | 0 0 0 0 0 0 1 4 0 2 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 1 0 0 0 0 | * * * * * * * * * * * * * * 2 * * * * * * | 0 0 0 0 0 0 0 1 1 0
.... .xo. .xx.&#x ♦ 0 4 2 0 | 0 0 0 0 0 2 2 4 0 0 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 0 2 2 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 2 * * * * * | 0 0 1 0 0 0 0 1 0 0
.oxo .... ....&#x ♦ 0 1 2 1 | 0 0 0 0 0 0 0 2 1 1 0 2 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 1 0 0 0 | * * * * * * * * * * * * * * * * 4 * * * * | 0 0 0 0 0 1 0 0 1 0
.... .... .xxx&#x ♦ 0 2 2 2 | 0 0 0 0 0 0 1 2 2 0 1 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 1 0 | * * * * * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 1 0 1 0
..xo ..ox ....&#x ♦ 0 0 2 2 | 0 0 0 0 0 0 0 0 0 1 0 4 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 | * * * * * * * * * * * * * * * * * * 2 * * | 0 0 0 0 0 1 0 0 0 1
..xo .... ..xx&#x ♦ 0 0 4 2 | 0 0 0 0 0 0 0 0 0 2 2 4 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 2 0 | * * * * * * * * * * * * * * * * * * * 2 * | 0 0 0 0 0 0 0 0 1 1
.... ..ox ..xx&#x ♦ 0 0 2 4 | 0 0 0 0 0 0 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 | * * * * * * * * * * * * * * * * * * * * 2 | 0 0 0 0 1 0 0 0 0 1
-------------------+---------+-----------------------------+---------------------------------------------+-------------------------------------------+--------------------
xo.. ox.. xx..&#x ♦ 4 4 0 0 | 2 2 8 0 0 2 2 0 0 0 0 0 0 0 | 1 4 4 4 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * *
x..o o..x x..x&#x ♦ 4 0 0 4 | 2 2 0 0 8 0 0 0 0 0 0 0 2 2 | 1 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 1 * * * * * * * *
.... oxo. xxx.&#x ♦ 2 4 2 0 | 0 1 4 2 0 2 2 4 0 0 1 0 0 0 | 0 0 2 2 1 0 0 0 4 0 0 1 0 2 2 0 0 0 0 0 0 0 | 0 0 1 0 0 0 2 2 0 0 0 0 0 0 0 1 0 0 0 0 0 | * * 2 * * * * * * *
xo.o .... xx.x&#x ♦ 4 2 0 2 | 2 2 4 0 4 0 1 0 2 0 0 0 0 1 | 1 2 0 2 0 2 0 2 0 4 0 0 0 0 0 1 0 0 0 0 0 0 | 0 1 0 0 1 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * * * 2 * * * * * *
.... o.ox x.xx&#x ♦ 2 0 2 4 | 0 1 0 2 4 0 0 0 0 0 1 4 2 2 | 0 0 0 0 1 0 2 2 0 0 4 0 0 0 0 0 0 0 0 2 2 1 | 0 0 0 0 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 1 | * * * * 2 * * * * *
xoxo oxox ....&#xr ♦ 2 2 2 2 | 1 0 4 2 4 1 0 4 2 1 0 4 1 0 | 0 2 2 0 0 2 2 0 4 4 4 0 2 2 0 0 4 0 2 2 0 0 | 1 0 0 1 0 0 2 0 2 0 2 0 4 1 0 0 2 0 1 0 0 | * * * * * 2 * * * *
.... .... xxxx&#x ♦ 2 2 2 2 | 0 1 2 2 2 0 1 2 2 0 1 2 0 1 | 0 0 0 1 1 0 0 1 2 2 2 0 0 0 1 1 2 0 0 0 1 0 | 0 0 0 0 0 0 0 1 0 1 0 1 2 0 0 0 0 1 0 0 0 | * * * * * * 4 * * *
.ox. .xo. .xx.&#x ♦ 0 4 4 0 | 0 0 0 0 0 2 2 8 0 2 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 4 4 4 0 0 1 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 | * * * * * * * 1 * *
.oxo .... .xxx&#x ♦ 0 2 4 2 | 0 0 0 0 0 0 1 4 2 2 2 4 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 1 4 1 2 0 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 2 0 1 0 | * * * * * * * * 2 *
..xo ..ox ..xx&#x ♦ 0 0 4 4 | 0 0 0 0 0 0 0 0 0 2 2 8 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 4 4 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * 1
or o... o... o... & | 16 | 1 1 4 1 | 1 6 4 1 6 | 2 6 4 6 2 | 2 4 1 2 ---------------------+----+----------+--------------+--------------+-------- x... .... .... & | 2 | 8 * * * | 1 4 0 0 0 | 2 4 2 0 0 | 2 2 1 0 .... .... x... & | 2 | * 8 * * ♦ 1 0 4 1 0 | 0 6 0 6 0 | 2 4 0 2 oo.. oo.. oo..&#x & | 2 | * * 32 * | 0 2 1 0 2 | 1 2 2 2 1 | 1 2 1 1 o.o. o.o. o.o.&#x & | 2 | * * * 8 | 0 0 0 1 4 | 0 0 2 4 2 | 0 2 1 2 ---------------------+----+----------+--------------+--------------+-------- x... .... x... & | 4 | 2 2 0 0 | 4 * * * * | 0 4 0 0 0 | 2 2 0 0 xo.. .... ....&#x & | 3 | 1 0 2 0 | * 32 * * * | 1 1 1 0 0 | 1 1 1 0 .... .... xx..&#x & | 4 | 0 2 2 0 | * * 16 * * | 0 2 0 2 0 | 1 2 0 1 .... .... x.x.&#x & | 4 | 0 2 0 2 | * * * 4 * | 0 0 0 4 0 | 0 2 0 2 ooo. ooo. ooo.&#x & | 3 | 0 0 2 1 | * * * * 32 | 0 0 1 1 1 | 0 1 1 1 ---------------------+----+----------+--------------+--------------+-------- xo.. ox.. ....&#x & ♦ 4 | 2 0 4 0 | 0 4 0 0 0 | 8 * * * * | 1 0 1 0 xo.. .... xx..&#x & ♦ 6 | 2 3 4 0 | 1 2 2 0 0 | * 16 * * * | 1 1 0 0 .... oxo. ....&#x & ♦ 4 | 1 0 4 1 | 0 2 0 0 2 | * * 16 * * | 0 1 1 0 .... .... xxx.&#x & ♦ 6 | 0 3 4 2 | 0 0 2 1 2 | * * * 16 * | 0 1 0 1 oooo oooo oooo&#x ♦ 4 | 0 0 4 2 | 0 0 0 0 4 | * * * * 8 | 0 0 1 1 ---------------------+----+----------+--------------+--------------+-------- xo.. ox.. xx..&#x & ♦ 8 | 4 4 8 0 | 2 8 4 0 0 | 2 4 0 0 0 | 4 * * * .... oxo. xxx.&#x & ♦ 8 | 2 4 8 2 | 1 4 4 1 4 | 0 2 2 2 0 | * 8 * * xoxo oxox ....&#xr ♦ 8 | 4 0 16 4 | 0 16 0 0 16 | 4 0 8 0 4 | * * 2 * .... .... xxxx&#x ♦ 8 | 0 4 8 4 | 0 0 4 2 8 | 0 0 0 4 2 | * * * 4
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