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Acronym
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oca (old: oc)
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Name
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octaexon,
7D simplex (α7),
pyrozett(id),
heptapetal pyramid,
vertex figure of ene,
(one of the) Delone cell(s) of lattice E7,
Gosset polytope 06
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|,>,O device
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line pyramid pyramid pyramid pyramid pyramid pyramid = |>>>>>>
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Circumradius
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sqrt(7)/4 = 0.661438
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Inradius
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1/sqrt(112) = 0.094491
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Coordinates
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-
(1/4, 1/4, 1/4, 1/4, 1/4, 1/4, 1/4)
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(1/4, 1/4, 1/4, -1/4, -1/4, -1/4, -1/4)
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(1/4, -1/4, -1/4, -1/4, -1/4, 1/4, 1/4)
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(1/4, -1/4, -1/4, 1/4, 1/4, -1/4, -1/4)
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(-1/4, 1/4, -1/4, 1/4, -1/4, 1/4, -1/4)
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(-1/4, 1/4, -1/4, -1/4, 1/4, -1/4, 1/4)
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(-1/4, -1/4, 1/4, 1/4, -1/4, -1/4, 1/4)
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(-1/4, -1/4, 1/4, -1/4, 1/4, 1/4, -1/4) ©
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Volume
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1/20160 = 0.000049603
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Surface
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sqrt(7)/720 = 0.0036747
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Rel. Roundness
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3 π3 sqrt(7)/38416 = 0.640631 %
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Dual
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(seldual, in different orientation)
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Dihedral angles
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- at hix between hop and hop: arccos(1/7) = 81.786789°
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Face vector
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8, 28, 56, 70, 56, 28, 8
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Confer
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- general polytopal classes:
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Wythoffian polyexa
simplex
noble polytopes
scalene
tettene
pennene
segmentoexa
fundamental lace prisms
Coxeter-Elte-Gosset polytopes
- analogs:
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regular simplex Sn
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External
links
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The above coordinates show that oca just reuses 8 out of the 128 vertices of a 1/2 downscaled hept.
In fact, for most n, which are divisible by 4, (esp. incl. all such n ≤ 664)
there is known to exist a Hadamard matrix.
The rows of which then would generalize this fact: Note that any consistent flip of sign to all entries of a row could be done onto any row within a Hadamard matrix,
while keeping it a Hadamard matrix still. Thence it becomes possible to wrangle it such that all first entries become equal.
This then shows that such matrices then represent the projective coordinates of a (scaled) (n-1)D simplex,
vertex-inscribed within an (n-1)D hypercube.
Incidence matrix according to Dynkin symbol
x3o3o3o3o3o3o
. . . . . . . | 8 ♦ 7 | 21 | 35 | 35 | 21 | 7
--------------+---+----+----+----+----+----+--
x . . . . . . | 2 | 28 ♦ 6 | 15 | 20 | 15 | 6
--------------+---+----+----+----+----+----+--
x3o . . . . . | 3 | 3 | 56 ♦ 5 | 10 | 10 | 5
--------------+---+----+----+----+----+----+--
x3o3o . . . . ♦ 4 | 6 | 4 | 70 ♦ 4 | 6 | 4
--------------+---+----+----+----+----+----+--
x3o3o3o . . . ♦ 5 | 10 | 10 | 5 | 56 | 3 | 3
--------------+---+----+----+----+----+----+--
x3o3o3o3o . . ♦ 6 | 15 | 20 | 15 | 6 | 28 | 2
--------------+---+----+----+----+----+----+--
x3o3o3o3o3o . ♦ 7 | 21 | 35 | 35 | 21 | 7 | 8
ox3oo3oo3oo3oo3oo&#x → height = 2/sqrt(7) = 0.755929
(pt || hop)
o.3o.3o.3o.3o.3o. | 1 * ♦ 7 0 | 21 0 | 35 0 | 35 0 | 21 0 | 7 0
.o3.o3.o3.o3.o3.o | * 7 ♦ 1 6 | 6 15 | 15 20 | 20 15 | 15 6 | 6 1
---------------------+-----+------+-------+-------+-------+------+----
oo3oo3oo3oo3oo3oo&#x | 1 1 | 7 * ♦ 6 0 | 15 0 | 20 0 | 15 0 | 6 0
.x .. .. .. .. .. | 0 2 | * 21 ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1
---------------------+-----+------+-------+-------+-------+------+----
ox .. .. .. .. ..&#x | 1 2 | 2 1 | 21 * ♦ 5 0 | 10 0 | 10 0 | 5 0
.x3.o .. .. .. .. | 0 3 | 0 3 | * 35 ♦ 1 4 | 4 6 | 6 4 | 4 1
---------------------+-----+------+-------+-------+-------+------+----
ox3oo .. .. .. ..&#x ♦ 1 3 | 3 3 | 3 1 | 35 * ♦ 4 0 | 6 0 | 4 0
.x3.o3.o .. .. .. ♦ 0 4 | 0 6 | 0 4 | * 35 ♦ 1 3 | 3 3 | 3 1
---------------------+-----+------+-------+-------+-------+------+----
ox3oo3oo .. .. ..&#x ♦ 1 4 | 4 6 | 6 4 | 4 1 | 35 * | 3 0 | 3 0
.x3.o3.o3.o .. .. ♦ 0 5 | 0 10 | 0 10 | 0 5 | * 21 | 1 2 | 2 1
---------------------+-----+------+-------+-------+-------+------+----
ox3oo3oo3oo .. ..&#x ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 | 21 * | 2 0
.x3.o3.o3.o3.o .. ♦ 0 6 | 0 15 | 0 20 | 0 15 | 0 6 | * 7 | 1 1
---------------------+-----+------+-------+-------+-------+------+----
ox3oo3oo3oo3oo ..&#x ♦ 1 6 | 6 15 | 15 20 | 20 15 | 15 6 | 6 1 | 7 *
.x3.o3.o3.o3.o3.o ♦ 0 7 | 0 21 | 0 35 | 0 35 | 0 21 | 0 7 | * 1
xo ox3oo3oo3oo3oo&#x → height = 1/sqrt(3) = 0.577350
(line || perp hix)
o. o.3o.3o.3o.3o. | 2 * ♦ 1 6 0 | 6 15 0 | 15 20 0 | 20 15 0 | 15 6 0 | 6 1
.o .o3.o3.o3.o3.o | * 6 ♦ 0 2 5 | 1 10 10 | 5 20 10 | 10 20 5 | 10 10 1 | 5 2
---------------------+-----+---------+---------+----------+---------+---------+----
x. .. .. .. .. .. | 2 0 | 1 * * ♦ 6 0 0 | 15 0 0 | 20 0 0 | 15 0 0 | 6 0
oo oo3oo3oo3oo3oo&#x | 1 1 | * 12 * ♦ 1 5 0 | 5 10 0 | 10 10 0 | 10 5 0 | 5 1
.. .x .. .. .. .. | 0 2 | * * 15 ♦ 0 2 4 | 1 8 6 | 4 12 4 | 6 8 1 | 4 2
---------------------+-----+---------+---------+----------+---------+---------+----
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | 6 * * ♦ 5 0 0 | 10 0 0 | 10 0 0 | 5 0
.. ox .. .. .. ..&#x | 1 2 | 0 2 1 | * 30 * ♦ 1 4 0 | 4 6 0 | 6 4 0 | 4 1
.. .x3.o .. .. .. | 0 3 | 0 0 3 | * * 20 ♦ 0 2 3 | 1 6 3 | 3 6 1 | 3 2
---------------------+-----+---------+---------+----------+---------+---------+----
xo ox .. .. .. ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 15 * * ♦ 4 0 0 | 6 0 0 | 4 0
.. ox3oo .. .. ..&#x ♦ 1 3 | 0 3 3 | 0 3 1 | * 40 * ♦ 1 3 0 | 3 3 0 | 3 1
.. .x3.o3.o .. .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * 15 ♦ 0 2 2 | 1 4 1 | 2 2
---------------------+-----+---------+---------+----------+---------+---------+----
xo ox3oo .. .. ..&#x ♦ 2 3 | 1 6 3 | 3 6 1 | 3 2 0 | 20 * * | 3 0 0 | 3 0
.. ox3oo3oo .. ..&#x ♦ 1 4 | 0 4 6 | 0 6 4 | 0 4 1 | * 30 * | 1 2 0 | 2 1
.. .x3.o3.o3.o .. ♦ 0 5 | 0 0 10 | 0 0 10 | 0 0 5 | * * 6 | 0 2 1 | 1 2
---------------------+-----+---------+---------+----------+---------+---------+----
xo ox3oo3oo .. ..&#x ♦ 2 4 | 1 8 6 | 4 12 4 | 6 8 1 | 4 2 0 | 15 * * | 2 0
.. ox3oo3oo3oo ..&#x ♦ 1 5 | 0 5 10 | 0 10 10 | 0 10 5 | 0 5 1 | * 12 * | 1 1
.. .x3.o3.o3.o3.o ♦ 0 6 | 0 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * * 1 | 0 2
---------------------+-----+---------+---------+----------+---------+---------+----
xo ox3oo3oo3oo ..&#x ♦ 2 5 | 1 10 10 | 5 20 10 | 10 20 5 | 10 10 1 | 5 2 0 | 6 *
.. ox3oo3oo3oo3oo&#x ♦ 1 6 | 0 6 15 | 0 15 20 | 0 20 15 | 0 15 6 | 0 6 1 | * 2
xo3oo ox3oo3oo3oo&#x → height = sqrt(4/15) = 0.516398
({3} || perp pen)
o.3o. o.3o.3o.3o. | 3 * ♦ 2 5 0 | 1 10 10 0 | 5 20 10 0 | 10 20 5 0 | 10 10 1 | 5 2
.o3.o .o3.o3.o3.o | * 5 ♦ 0 3 4 | 0 3 12 6 | 1 12 18 4 | 4 18 12 1 | 6 12 3 | 4 3
---------------------+-----+---------+------------+-----------+------------+---------+----
x. .. .. .. .. .. | 2 0 | 3 * * ♦ 1 5 0 0 | 5 10 0 0 | 10 10 0 0 | 10 5 0 | 5 1
oo3oo oo3oo3oo3oo&#x | 1 1 | * 15 * ♦ 0 2 4 0 | 1 8 6 0 | 4 12 4 0 | 6 8 1 | 4 2
.. .. .x .. .. .. | 0 2 | * * 10 ♦ 0 0 3 3 | 0 3 9 3 | 1 9 9 1 | 3 9 3 | 3 3
---------------------+-----+---------+------------+-----------+------------+---------+----
x.3o. .. .. .. .. | 3 0 | 3 0 0 | 1 * * * ♦ 5 0 0 0 | 10 0 0 0 | 10 0 0 | 5 0
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 15 * * ♦ 1 4 0 0 | 4 6 0 0 | 6 4 0 | 4 1
.. .. ox .. .. ..&#x | 1 2 | 0 2 1 | * * 30 * ♦ 0 2 3 0 | 1 6 3 0 | 3 6 1 | 3 2
.. .. .x3.o .. .. | 0 3 | 0 0 3 | * * * 10 ♦ 0 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3
---------------------+-----+---------+------------+-----------+------------+---------+----
xo3oo .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | 5 * * * ♦ 4 0 0 0 | 6 0 0 | 4 0
xo .. ox .. .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * 30 * * ♦ 1 3 0 0 | 3 3 0 | 3 1
.. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * 30 * ♦ 0 2 2 0 | 1 4 1 | 2 2
.. .. .x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * 5 ♦ 0 0 3 1 | 0 3 3 | 1 3
---------------------+-----+---------+------------+-----------+------------+---------+----
xo3oo ox .. .. ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 2 3 0 0 | 10 * * * | 3 0 0 | 3 0
xo .. ox3oo .. ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 3 2 0 | * 30 * * | 1 2 0 | 2 1
.. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 4 1 | * * 15 * | 0 2 1 | 1 2
.. .. .x3.o3.o3.o ♦ 0 5 | 0 0 10 | 0 0 0 10 | 0 0 0 5 | * * * 1 | 0 0 3 | 0 3
---------------------+-----+---------+------------+-----------+------------+---------+----
xo3oo ox3oo .. ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 | 3 9 3 0 | 3 3 0 0 | 10 * * | 2 0
xo .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 6 8 1 | 0 4 2 0 | * 15 * | 1 1
.. .. ox3oo3oo3oo&#x ♦ 1 5 | 0 5 10 | 0 0 10 10 | 0 0 10 5 | 0 0 5 1 | * * 3 | 0 2
---------------------+-----+---------+------------+-----------+------------+---------+----
xo3oo ox3oo3oo ..&#x ♦ 3 4 | 3 12 6 | 1 12 18 4 | 4 18 12 1 | 6 12 3 0 | 4 3 0 | 5 *
xo .. ox3oo3oo3oo&#x ♦ 2 5 | 1 10 10 | 0 5 20 10 | 0 10 20 5 | 0 10 10 1 | 0 5 2 | * 3
xo3oo3oo ox3oo3oo&#x → height = 1/2
(tet || perp tet)
o.3o.3o. o.3o.3o. | 4 * ♦ 3 4 0 | 3 12 6 0 | 1 12 18 4 0 | 4 18 12 1 | 6 12 3 | 4 3
.o3.o3.o .o3.o3.o | * 4 ♦ 0 4 3 | 0 6 12 3 | 0 4 18 12 1 | 1 12 18 4 | 3 12 6 | 3 4
---------------------+-----+--------+-----------+--------------+-----------+--------+----
x. .. .. .. .. .. | 2 0 | 6 * * ♦ 2 4 0 0 | 1 6 8 0 0 | 4 12 4 0 | 6 8 1 | 4 2
oo3oo3oo oo3oo3oo&#x | 1 1 | * 16 * ♦ 0 3 3 0 | 0 3 9 3 0 | 1 9 9 1 | 3 9 3 | 3 3
.. .. .. .x .. .. | 0 2 | * * 6 ♦ 0 0 4 2 | 0 0 6 8 1 | 0 4 12 4 | 1 8 6 | 2 4
---------------------+-----+--------+-----------+--------------+-----------+--------+----
x.3o. .. .. .. .. | 3 0 | 3 0 0 | 4 * * * ♦ 1 4 0 0 0 | 4 6 0 0 | 6 4 0 | 4 1
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 24 * * ♦ 0 2 3 0 0 | 1 6 3 0 | 3 6 1 | 3 2
.. .. .. ox .. ..&#x | 1 2 | 0 2 1 | * * 24 * ♦ 0 0 3 2 0 | 0 3 6 1 | 1 6 3 | 2 3
.. .. .. .x3.o .. | 0 3 | 0 0 3 | * * * 4 ♦ 0 0 0 4 1 | 0 0 6 4 | 0 4 6 | 1 4
---------------------+-----+--------+-----------+--------------+-----------+--------+----
x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 1 * * * * ♦ 4 0 0 0 | 6 0 0 | 4 0
xo3oo .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * 16 * * * ♦ 1 3 0 0 | 3 3 0 | 3 1
xo .. .. ox .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * 36 * * ♦ 0 2 2 0 | 1 4 1 | 2 2
.. .. .. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * 16 * ♦ 0 0 3 1 | 0 3 3 | 1 3
.. .. .. .x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * 1 ♦ 0 0 0 4 | 0 0 6 | 0 4
---------------------+-----+--------+-----------+--------------+-----------+--------+----
xo3oo3oo .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 1 4 0 0 0 | 4 * * * | 3 0 0 | 3 0
xo3oo .. ox .. ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 0 2 3 0 0 | * 24 * * | 1 2 0 | 2 1
xo .. .. ox3oo ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 0 3 2 0 | * * 24 * | 0 2 1 | 1 2
.. .. .. ox3oo3oo&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 4 1 | * * * 4 | 0 0 3 | 0 3
---------------------+-----+--------+-----------+--------------+-----------+--------+----
xo3oo3oo ox .. ..&#x ♦ 4 2 | 6 8 1 | 4 12 4 0 | 1 8 6 0 0 | 2 4 0 0 | 6 * * | 2 0
xo3oo .. ox3oo ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 | 0 3 9 3 0 | 0 3 3 0 | * 16 * | 1 1
xo .. .. ox3oo3oo&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 0 6 8 1 | 0 0 4 2 | * * 6 | 0 2
---------------------+-----+--------+-----------+--------------+-----------+--------+----
xo3oo3oo ox3oo ..&#x ♦ 4 3 | 6 12 3 | 4 18 12 1 | 1 12 18 4 0 | 3 12 6 0 | 3 4 0 | 4 *
xo3oo .. ox3oo3oo&#x ♦ 3 4 | 3 12 6 | 1 12 18 4 | 0 4 18 12 1 | 0 6 12 3 | 0 4 3 | * 4
or
o.3o.3o. o.3o.3o. & | 8 ♦ 3 4 | 3 18 | 1 16 18 | 5 30 | 9 12 | 7
-----------------------+---+-------+------+---------+------+-------+--
x. .. .. .. .. .. & | 2 | 12 * ♦ 2 4 | 1 8 6 | 4 16 | 7 8 | 6
oo3oo3oo oo3oo3oo&#x | 2 | * 16 ♦ 0 6 | 0 6 9 | 2 18 | 6 9 | 6
-----------------------+---+-------+------+---------+------+-------+--
x.3o. .. .. .. .. & | 3 | 3 0 | 8 * ♦ 1 4 0 | 4 6 | 6 4 | 5
xo .. .. .. .. ..&#x & | 3 | 1 2 | * 48 ♦ 0 2 3 | 1 9 | 4 6 | 5
-----------------------+---+-------+------+---------+------+-------+--
x.3o.3o. .. .. .. & ♦ 4 | 6 0 | 4 0 | 2 * * ♦ 4 0 | 6 0 | 4
xo3oo .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * 32 * ♦ 1 3 | 3 3 | 4
xo .. .. ox .. ..&#x ♦ 4 | 2 4 | 0 4 | * * 36 ♦ 0 4 | 2 4 | 4
-----------------------+---+-------+------+---------+------+-------+--
xo3oo3oo .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 1 4 0 | 8 * | 3 0 | 3
xo3oo .. ox .. ..&#x & ♦ 5 | 4 6 | 1 9 | 0 2 3 | * 48 | 1 2 | 3
-----------------------+---+-------+------+---------+------+-------+--
xo3oo3oo ox .. ..&#x & ♦ 6 | 7 8 | 4 16 | 1 8 6 | 2 4 | 12 * | 2
xo3oo .. ox3oo ..&#x ♦ 6 | 6 9 | 2 18 | 0 6 9 | 0 6 | * 16 | 2
-----------------------+---+-------+------+---------+------+-------+--
xo3oo3oo ox3oo ..&#x & ♦ 7 | 9 12 | 5 30 | 1 16 18 | 3 18 | 3 4 | 8
xoo oox3ooo3ooo3ooo&#x → height(1,2) = sqrt(3)/2 = 0.866025
height(1,3) = sqrt(7/20) = 0.591608
height(2,3) = sqrt(3/5) = 0.774597
( (line || pt) || perp pen)
o.. o..3o..3o..3o.. | 2 * * ♦ 1 1 5 0 0 | 1 5 10 5 0 0 | 10 10 5 10 0 0 | 10 5 10 10 0 0 | 5 1 10 5 0 | 1 5 1
.o. .o.3.o.3.o.3.o. | * 1 * ♦ 0 2 0 5 0 | 1 0 0 10 10 0 | 0 0 5 20 10 0 | 0 0 10 20 5 0 | 0 0 10 10 1 | 0 5 2
..o ..o3..o3..o3..o | * * 5 ♦ 0 0 2 1 4 | 0 1 8 2 4 6 | 4 12 1 8 6 4 | 6 8 4 12 4 1 | 4 2 6 8 1 | 1 4 2
-----------------------+-------+-------------+-----------------+-----------------+-----------------+-------------+------
x.. ... ... ... ... | 2 0 0 | 1 * * * * ♦ 1 5 0 0 0 0 | 10 0 5 0 0 0 | 10 0 10 0 0 0 | 5 0 10 0 0 | 1 5 0
oo. oo.3oo.3oo.3oo.&#x | 1 1 0 | * 2 * * * ♦ 1 0 0 5 0 0 | 0 0 5 10 0 0 | 0 0 10 10 0 0 | 0 0 10 5 0 | 0 5 1
o.o o.o3o.o3o.o3o.o&#x | 1 0 1 | * * 10 * * ♦ 0 1 4 1 0 0 | 4 6 1 4 0 0 | 6 4 4 6 0 0 | 4 1 6 4 0 | 1 4 1
.oo .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * 5 * ♦ 0 0 0 2 4 0 | 0 0 1 8 6 0 | 0 0 4 12 4 0 | 0 0 6 8 1 | 0 4 2
... ..x ... ... ... | 0 0 2 | * * * * 10 ♦ 0 0 2 0 1 3 | 1 6 0 2 3 3 | 3 6 1 6 3 1 | 3 2 3 6 1 | 1 3 2
-----------------------+-------+-------------+-----------------+-----------------+-----------------+-------------+------
xo. ... ... ... ...&#x | 2 1 0 | 1 2 0 0 0 | 1 * * * * * ♦ 0 0 5 0 0 0 | 0 0 10 0 0 0 | 0 0 10 0 0 | 0 5 0
x.o ... ... ... ...&#x | 2 0 1 | 1 0 2 0 0 | * 5 * * * * ♦ 4 0 1 0 0 0 | 6 0 4 0 0 0 | 4 0 6 0 0 | 1 4 0
... o.x ... ... ...&#x | 1 0 2 | 0 0 2 0 1 | * * 20 * * * ♦ 1 3 0 1 0 0 | 3 3 1 3 0 0 | 3 1 3 3 0 | 1 3 1
ooo ooo3ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 1 0 | * * * 10 * * ♦ 0 0 1 4 0 0 | 0 0 4 6 0 0 | 0 0 6 4 0 | 0 4 1
... .ox ... ... ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * 10 * ♦ 0 0 0 2 3 0 | 0 0 1 6 3 0 | 0 0 3 6 1 | 0 3 2
... ..x3..o ... ... | 0 0 3 | 0 0 0 0 3 | * * * * * 10 ♦ 0 2 0 0 1 2 | 1 4 0 2 2 1 | 2 2 1 4 1 | 1 2 2
-----------------------+-------+-------------+-----------------+-----------------+-----------------+-------------+------
x.o o.x ... ... ...&#x ♦ 2 0 2 | 1 0 4 0 1 | 0 2 2 0 0 0 | 10 * * * * * ♦ 3 0 1 0 0 0 | 3 0 3 0 0 | 1 3 0
... o.x3o.o ... ...&#x ♦ 1 0 3 | 0 0 3 0 3 | 0 0 3 0 0 1 | * 20 * * * * ♦ 1 2 0 1 0 0 | 2 1 1 2 0 | 1 2 1
xoo ... ... ... ...&#x ♦ 2 1 1 | 1 2 2 1 0 | 1 1 0 2 0 0 | * * 5 * * * ♦ 0 0 4 0 0 0 | 0 0 6 0 0 | 0 4 0
... oox ... ... ...&#x ♦ 1 1 2 | 0 1 2 2 1 | 0 0 1 2 1 0 | * * * 20 * * ♦ 0 0 1 3 0 0 | 0 0 3 3 0 | 0 3 1
... .ox3.oo ... ...&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 3 1 | * * * * 10 * ♦ 0 0 0 2 2 0 | 0 0 1 4 1 | 0 2 2
... ..x3..o3..o ... ♦ 0 0 4 | 0 0 0 0 6 | 0 0 0 0 0 4 | * * * * * 5 ♦ 0 2 0 0 1 1 | 1 2 0 2 1 | 1 1 2
-----------------------+-------+-------------+-----------------+-----------------+-----------------+-------------+------
x.o o.x3o.o ... ...&#x ♦ 2 0 3 | 1 0 6 0 3 | 0 3 6 0 0 1 | 3 2 0 0 0 0 | 10 * * * * * | 2 0 1 0 0 | 1 2 0
... o.x3o.o3o.o ...&#x ♦ 1 0 4 | 0 0 4 0 6 | 0 0 6 0 0 4 | 0 4 0 0 0 1 | * 10 * * * * | 1 1 0 1 0 | 1 1 1
xoo oox ... ... ...&#x ♦ 2 1 2 | 1 2 4 2 1 | 1 2 2 4 1 0 | 1 0 2 2 0 0 | * * 10 * * * | 0 0 3 0 0 | 0 3 0
... oox3ooo ... ...&#x ♦ 1 1 3 | 0 1 3 3 3 | 0 0 3 3 3 1 | 0 1 0 3 1 0 | * * * 20 * * | 0 0 1 2 0 | 0 2 1
... .ox3.oo3.oo ...&#x ♦ 0 1 4 | 0 0 0 4 6 | 0 0 0 0 6 4 | 0 0 0 0 4 1 | * * * * 5 * | 0 0 0 2 1 | 0 1 2
... ..x3..o3..o3..o ♦ 0 0 5 | 0 0 0 0 10 | 0 0 0 0 0 10 | 0 0 0 0 0 5 | * * * * * 1 | 0 2 0 0 1 | 1 0 2
-----------------------+-------+-------------+-----------------+-----------------+-----------------+-------------+------
x.o o.x3o.o3o.o ...&#x ♦ 2 0 4 | 1 0 8 0 6 | 0 4 12 0 0 4 | 6 8 0 0 0 1 | 4 2 0 0 0 0 | 5 * * * * | 1 1 0
... o.x3o.o3o.o3o.o&#x ♦ 1 0 5 | 0 0 5 0 10 | 0 0 10 0 0 10 | 0 10 0 0 0 5 | 0 5 0 0 0 1 | * 2 * * * | 1 0 1
xoo oox3ooo ... ...&#x ♦ 2 1 3 | 1 2 6 3 3 | 1 3 6 6 3 1 | 3 2 3 6 1 0 | 1 0 3 2 0 0 | * * 10 * * | 0 2 0
... oox3ooo3ooo ...&#x ♦ 1 1 4 | 0 1 4 4 6 | 0 0 6 4 6 4 | 0 4 0 6 4 1 | 0 1 0 4 1 0 | * * * 10 * | 0 1 1
... .ox3.oo3.oo3.oo&#x ♦ 0 1 5 | 0 0 0 5 10 | 0 0 0 0 10 10 | 0 0 0 0 10 5 | 0 0 0 0 5 1 | * * * * 1 | 0 0 2
-----------------------+-------+-------------+-----------------+-----------------+-----------------+-------------+------
x.o o.x3o.o3o.o3o.o&#x ♦ 2 0 5 | 1 0 10 0 10 | 0 5 20 0 0 10 | 10 20 0 0 0 5 | 10 10 0 0 0 1 | 5 2 0 0 0 | 1 * *
xoo oox3ooo3ooo ...&#x ♦ 2 1 4 | 1 2 8 4 6 | 1 4 12 8 6 4 | 6 8 4 12 4 1 | 4 2 6 8 1 0 | 1 0 4 2 0 | * 5 *
... oox3ooo3ooo3ooo&#x ♦ 1 1 5 | 0 1 5 5 10 | 0 0 10 5 10 10 | 0 10 0 10 10 5 | 0 5 0 10 5 1 | 0 1 0 5 1 | * * 2
oxo3ooo oox3ooo3ooo&#x → height(1,2) = sqrt(2/3) = 0.816497
height(1,3) = sqrt(5/8) = 0.790569
height(2,3) = sqrt(7/24) = 0.540062
( (pt || {3}) || perp tet)
o..3o.. o..3o..3o.. | 1 * * ♦ 3 4 0 0 0 | 3 6 12 0 0 0 0 | 12 1 18 4 0 0 0 0 | 4 18 12 1 0 0 0 | 6 12 3 0 0 | 4 3 0
.o.3.o. .o.3.o.3.o. | * 3 * ♦ 1 0 2 4 0 | 2 0 4 1 8 6 0 | 8 1 6 0 4 12 4 0 | 4 12 4 0 6 8 1 | 6 8 1 4 2 | 4 2 1
..o3..o ..o3..o3..o | * * 4 ♦ 0 1 0 3 3 | 0 3 3 0 3 9 3 | 3 0 9 3 1 9 9 1 | 1 9 9 1 3 9 3 | 3 9 3 3 3 | 3 3 1
-----------------------+-------+------------+------------------+---------------------+------------------+------------+------
oo.3oo. oo.3oo.3oo.&#x | 1 1 0 | 3 * * * * ♦ 2 0 4 0 0 0 0 | 8 1 6 0 0 0 0 0 | 4 12 4 0 0 0 0 | 6 8 1 0 0 | 4 2 0
o.o3o.o o.o3o.o3o.o&#x | 1 0 1 | * 4 * * * ♦ 0 3 3 0 0 0 0 | 3 0 9 3 0 0 0 0 | 1 9 9 1 0 0 0 | 3 9 3 0 0 | 3 3 0
.x. ... ... ... ... | 0 2 0 | * * 3 * * ♦ 1 0 0 1 4 0 0 | 4 1 0 0 4 6 0 0 | 4 6 0 0 6 4 0 | 6 4 0 4 1 | 4 1 1
.oo3.oo .oo3.oo3.oo&#x | 0 1 1 | * * * 12 * ♦ 0 0 1 0 2 3 0 | 2 0 3 0 1 6 3 0 | 1 6 3 0 3 6 1 | 3 6 1 3 2 | 3 2 1
... ... ..x ... ... | 0 0 2 | * * * * 6 ♦ 0 1 0 0 0 3 2 | 0 0 3 2 0 3 6 1 | 0 3 6 1 1 6 3 | 1 6 3 2 3 | 2 3 1
-----------------------+-------+------------+------------------+---------------------+------------------+------------+------
ox. ... ... ... ...&#x | 1 2 0 | 2 0 1 0 0 | 3 * * * * * * ♦ 4 1 0 0 0 0 0 0 | 4 6 0 0 0 0 0 | 6 4 0 0 0 | 4 1 0
... ... o.x ... ...&#x | 1 0 2 | 0 2 0 0 1 | * 6 * * * * * ♦ 0 0 3 2 0 0 0 0 | 0 3 6 1 0 0 0 | 1 6 3 0 0 | 2 3 0
ooo3ooo ooo3ooo3ooo&#x | 1 1 1 | 1 1 0 1 0 | * * 12 * * * * ♦ 2 0 3 0 0 0 0 0 | 1 6 3 0 0 0 0 | 3 6 1 0 0 | 3 2 0
.x.3.o. ... ... ... | 0 3 0 | 0 0 3 0 0 | * * * 1 * * * ♦ 0 1 0 0 4 0 0 0 | 4 0 0 0 6 0 0 | 6 0 0 4 0 | 4 0 1
.xo ... ... ... ...&#x | 0 2 1 | 0 0 1 2 0 | * * * * 12 * * ♦ 1 0 0 0 1 3 0 0 | 1 3 0 0 3 3 0 | 3 3 0 3 1 | 3 1 1
... ... .ox ... ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 18 * ♦ 0 0 1 0 0 2 2 0 | 0 2 2 0 1 4 1 | 1 4 1 2 2 | 2 2 1
... ... ..x3..o ... | 0 0 3 | 0 0 0 0 3 | * * * * * * 4 ♦ 0 0 0 1 0 0 3 1 | 0 0 3 1 0 3 3 | 0 3 3 1 3 | 1 3 1
-----------------------+-------+------------+------------------+---------------------+------------------+------------+------
oxo ... ... ... ...&#x ♦ 1 2 1 | 2 1 1 2 0 | 1 0 2 0 1 0 0 | 12 * * * * * * * ♦ 1 3 0 0 0 0 0 | 3 3 0 0 0 | 3 1 0
ox.3oo. ... ... ...&#x ♦ 1 3 0 | 3 0 3 0 0 | 3 0 0 1 0 0 0 | * 1 * * * * * * ♦ 4 0 0 0 0 0 0 | 6 0 0 0 0 | 4 0 0
... ... oox ... ...&#x ♦ 1 1 2 | 1 2 0 2 1 | 0 1 2 0 0 1 0 | * * 18 * * * * * ♦ 0 2 2 0 0 0 0 | 1 4 1 0 0 | 2 2 0
... ... o.x3o.o ...&#x ♦ 1 0 3 | 0 3 0 0 3 | 0 3 0 0 0 0 1 | * * * 4 * * * * ♦ 0 0 3 1 0 0 0 | 0 3 3 0 0 | 1 3 0
.xo3.oo ... ... ...&#x ♦ 0 3 1 | 0 0 3 3 0 | 0 0 0 1 3 0 0 | * * * * 4 * * * ♦ 1 0 0 0 3 0 0 | 3 0 0 3 0 | 3 0 1
.xo ... .ox ... ...&#x ♦ 0 2 2 | 0 0 1 4 1 | 0 0 0 0 2 2 0 | * * * * * 18 * * ♦ 0 1 0 0 1 2 0 | 1 2 0 2 1 | 2 1 1
... ... .ox3.oo ...&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 0 3 1 | * * * * * * 12 * ♦ 0 0 1 0 0 2 1 | 0 2 1 1 2 | 1 2 1
... ... ..x3..o3..o ♦ 0 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * * 1 ♦ 0 0 0 1 0 0 3 | 0 0 3 0 3 | 0 3 1
-----------------------+-------+------------+------------------+---------------------+------------------+------------+------
oxo3ooo ... ... ...&#x ♦ 1 3 1 | 3 1 3 3 0 | 3 0 3 1 3 0 0 | 3 1 0 0 1 0 0 0 | 4 * * * * * * | 3 0 0 0 0 | 3 0 0
oxo ... oox ... ...&#x ♦ 1 2 2 | 2 2 1 4 1 | 1 1 4 0 2 2 0 | 2 0 2 0 0 1 0 0 | * 18 * * * * * | 1 2 0 0 0 | 2 1 0
... ... oox3ooo ...&#x ♦ 1 1 3 | 1 3 0 3 3 | 0 3 3 0 0 3 1 | 0 0 3 1 0 0 1 0 | * * 12 * * * * | 0 2 1 0 0 | 1 2 0
... ... o.x3o.o3o.o&#x ♦ 1 0 4 | 0 4 0 0 6 | 0 6 0 0 0 0 4 | 0 0 0 4 0 0 0 1 | * * * 1 * * * | 0 0 3 0 0 | 0 3 0
.xo3.oo .ox ... ...&#x ♦ 0 3 2 | 0 0 3 6 1 | 0 0 0 1 6 3 0 | 0 0 0 0 2 3 0 0 | * * * * 6 * * | 1 0 0 2 0 | 2 0 1
.xo ... .ox3.oo ...&#x ♦ 0 2 3 | 0 0 1 6 3 | 0 0 0 0 3 6 1 | 0 0 0 0 0 3 2 0 | * * * * * 12 * | 0 1 0 1 1 | 1 1 1
... ... .ox3.oo3.oo&#x ♦ 0 1 4 | 0 0 0 4 6 | 0 0 0 0 0 6 4 | 0 0 0 0 0 0 4 1 | * * * * * * 3 | 0 0 1 0 2 | 0 2 1
-----------------------+-------+------------+------------------+---------------------+------------------+------------+------
oxo3ooo oox ... ...&#x ♦ 1 3 2 | 3 2 3 6 1 | 3 1 6 1 6 3 0 | 6 1 3 0 2 3 0 0 | 2 3 0 0 1 0 0 | 6 * * * * | 2 0 0
oxo ... oox3ooo ...&#x ♦ 1 2 3 | 2 3 1 6 3 | 1 3 6 0 3 6 1 | 3 0 6 1 0 3 2 0 | 0 3 2 0 0 1 0 | * 12 * * * | 1 1 0
... ... oox3ooo3ooo&#x ♦ 1 1 4 | 1 4 0 4 6 | 0 6 4 0 0 6 4 | 0 0 6 4 0 0 4 1 | 0 0 4 1 0 0 1 | * * 3 * * | 0 2 0
.xo3.oo .ox3.oo ...&#x ♦ 0 3 3 | 0 0 3 9 3 | 0 0 0 1 9 9 1 | 0 0 0 0 3 9 3 0 | 0 0 0 0 3 3 0 | * * * 4 * | 1 0 1
.xo ... .ox3.oo3.oo&#x ♦ 0 2 4 | 0 0 1 8 6 | 0 0 0 0 4 12 4 | 0 0 0 0 0 6 8 1 | 0 0 0 0 0 4 2 | * * * * 3 | 0 1 1
-----------------------+-------+------------+------------------+---------------------+------------------+------------+------
oxo3ooo oox3ooo ...&#x ♦ 1 3 3 | 3 3 3 9 3 | 3 3 9 1 9 9 1 | 9 1 9 1 3 9 3 0 | 3 9 3 0 3 3 0 | 3 3 0 1 0 | 4 * *
oxo ... oox3ooo3ooo&#x ♦ 1 2 4 | 2 4 1 8 6 | 1 6 8 0 4 12 4 | 4 0 12 4 0 6 8 1 | 0 6 8 1 0 4 2 | 0 4 2 0 1 | * 3 *
.xo3.oo .ox3.oo3.oo&#x ♦ 0 3 4 | 0 0 3 12 6 | 0 0 0 1 12 18 4 | 0 0 0 0 4 18 12 1 | 0 0 0 0 6 12 3 | 0 0 0 4 3 | * * 1
oxo xoo3ooo oox3ooo&#x → height(1,2) = height(2,3) = sqrt(5/12) = 0.645497
height(1,3) = 1/sqrt(3) = 0.577350
( (line || perp {3}) || perp {3})
o.. o..3o.. o..3o.. | 3 * * ♦ 2 2 3 0 0 0 | 1 1 4 6 3 6 0 0 0 | 3 2 12 2 3 6 6 1 0 0 | 6 1 3 6 3 12 2 2 0 | 3 6 1 6 1 4 | 3 2 2
.o. .o.3.o. .o.3.o. | * 2 * ♦ 0 3 0 1 3 0 | 0 3 3 0 0 9 3 3 0 | 9 3 9 1 0 0 9 0 3 1 | 9 1 9 3 0 9 0 3 1 | 3 9 3 3 0 3 | 3 3 1
..o ..o3..o ..o3..o | * * 3 ♦ 0 0 3 0 2 2 | 0 0 0 3 6 6 1 4 1 | 3 0 6 0 1 6 12 3 2 2 | 3 0 6 2 2 12 3 6 1 | 1 6 3 4 1 6 | 2 3 2
-----------------------+-------+-------------+--------------------+-----------------------+--------------------+-------------+------
... x.. ... ... ... | 2 0 0 | 3 * * * * * ♦ 1 0 2 3 0 0 0 0 0 | 0 1 6 2 3 3 0 0 0 0 | 3 1 0 6 3 6 1 0 0 | 3 3 0 6 1 2 | 3 1 2
oo. oo.3oo. oo.3oo.&#x | 1 1 0 | * 6 * * * * ♦ 0 1 2 0 0 3 0 0 0 | 3 2 6 1 0 0 3 0 0 0 | 6 1 3 3 0 6 0 1 0 | 3 6 1 3 0 2 | 3 2 1
o.o o.o3o.o o.o3o.o&#x | 1 0 1 | * * 9 * * * ♦ 0 0 0 2 2 2 0 0 0 | 1 0 4 0 1 4 4 1 0 0 | 2 0 2 2 2 8 2 2 0 | 1 4 1 4 1 4 | 2 2 2
.x. ... ... ... ... | 0 2 0 | * * * 1 * * ♦ 0 3 0 0 0 0 3 0 0 | 9 3 0 0 0 0 0 0 3 0 | 9 1 9 0 0 0 0 0 1 | 3 9 3 0 0 0 | 3 3 0
.oo .oo3.oo .oo3.oo&#x | 0 1 1 | * * * * 6 * ♦ 0 0 0 0 0 3 1 2 0 | 3 0 3 0 0 0 6 0 2 1 | 3 0 6 1 0 6 0 3 1 | 1 6 3 2 0 3 | 2 3 1
... ... ... ..x ... | 0 0 2 | * * * * * 3 ♦ 0 0 0 0 3 0 0 2 1 | 0 0 0 0 0 3 6 3 1 2 | 0 0 3 0 1 6 3 6 1 | 0 3 3 2 1 6 | 1 3 2
-----------------------+-------+-------------+--------------------+-----------------------+--------------------+-------------+------
... x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * ♦ 0 0 0 2 3 0 0 0 0 0 | 0 1 0 6 3 0 0 0 0 | 3 0 0 6 1 0 | 3 0 2
ox. ... ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 3 * * * * * * * ♦ 3 2 0 0 0 0 0 0 0 0 | 6 1 3 0 0 0 0 0 0 | 3 6 1 0 0 0 | 3 2 0
... xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * * 6 * * * * * * ♦ 0 1 3 1 0 0 0 0 0 0 | 3 1 0 3 0 3 0 0 0 | 3 3 0 3 0 1 | 3 1 1
... x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 9 * * * * * ♦ 0 0 2 0 1 2 0 0 0 0 | 1 0 0 2 2 4 1 0 0 | 1 2 0 4 1 2 | 2 1 2
... ... ... o.x ...&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 9 * * * * ♦ 0 0 0 0 0 2 2 1 0 0 | 0 0 1 0 1 4 2 2 0 | 0 2 1 2 1 4 | 1 2 2
ooo ooo3ooo ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 18 * * * ♦ 1 0 2 0 0 0 2 0 0 0 | 2 0 2 1 0 4 0 1 0 | 1 4 1 2 0 2 | 2 2 1
.xo ... ... ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * 3 * * ♦ 3 0 0 0 0 0 0 0 2 0 | 3 0 6 0 0 0 0 0 1 | 1 6 3 0 0 0 | 2 3 0
... ... ... .ox ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * 6 * ♦ 0 0 0 0 0 0 3 0 1 1 | 0 0 3 0 0 3 0 3 1 | 0 3 3 1 0 3 | 1 3 1
... ... ... ..x3..o | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 1 ♦ 0 0 0 0 0 0 0 3 0 2 | 0 0 0 0 0 0 3 6 1 | 0 0 3 0 1 6 | 0 3 2
-----------------------+-------+-------------+--------------------+-----------------------+--------------------+-------------+------
oxo ... ... ... ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 1 0 0 0 2 1 0 0 | 9 * * * * * * * * * ♦ 2 0 2 0 0 0 0 0 0 | 1 4 1 0 0 0 | 2 2 0
ox. xo. ... ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 2 0 0 0 0 0 0 | * 3 * * * * * * * * ♦ 3 1 0 0 0 0 0 0 0 | 3 3 0 0 0 0 | 3 1 0
... xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 0 1 1 0 2 0 0 0 | * * 18 * * * * * * * ♦ 1 0 0 1 0 2 0 0 0 | 1 2 0 2 0 1 | 2 1 1
... xo.3oo. ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 0 3 0 0 0 0 0 0 | * * * 2 * * * * * * ♦ 0 1 0 3 0 0 0 0 0 | 3 0 0 3 0 0 | 3 0 1
... x.o3o.o ... ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 | 1 0 0 3 0 0 0 0 0 | * * * * 3 * * * * * ♦ 0 0 0 2 2 0 0 0 0 | 1 0 0 4 1 0 | 2 0 2
... x.o ... o.x ...&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 0 2 2 0 0 0 0 | * * * * * 9 * * * * ♦ 0 0 0 0 1 2 1 0 0 | 0 1 0 2 1 2 | 1 1 2
... ... ... oox ...&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 0 1 2 0 1 0 | * * * * * * 18 * * * ♦ 0 0 1 0 0 2 0 1 0 | 0 2 1 1 0 2 | 1 2 1
... ... ... o.x3o.o&#x ♦ 1 0 3 | 0 0 3 0 0 3 | 0 0 0 0 3 0 0 0 1 | * * * * * * * 3 * * ♦ 0 0 0 0 0 0 2 2 0 | 0 0 1 0 1 4 | 0 2 2
.xo ... ... .ox ...&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 0 2 2 0 | * * * * * * * * 3 * ♦ 0 0 3 0 0 0 0 0 1 | 0 3 3 0 0 0 | 1 3 0
... ... ... .ox3.oo&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 3 1 | * * * * * * * * * 2 ♦ 0 0 0 0 0 0 0 3 1 | 0 0 3 0 0 3 | 0 3 1
-----------------------+-------+-------------+--------------------+-----------------------+--------------------+-------------+------
oxo xoo ... ... ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 0 2 2 1 0 4 1 0 0 | 2 1 2 0 0 0 0 0 0 0 | 9 * * * * * * * * | 1 2 0 0 0 0 | 2 1 0
ox. xo.3oo. ... ...&#x ♦ 3 2 0 | 3 6 0 1 0 0 | 1 3 6 0 0 0 0 0 0 | 0 3 0 2 0 0 0 0 0 0 | * 1 * * * * * * * | 3 0 0 0 0 0 | 3 0 0
oxo ... ... oox ...&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 1 0 0 1 4 2 2 0 | 2 0 0 0 0 0 2 0 1 0 | * * 9 * * * * * * | 0 2 1 0 0 0 | 1 2 0
... xoo3ooo ... ...&#x ♦ 3 1 1 | 3 3 3 0 1 0 | 1 0 3 3 0 3 0 0 0 | 0 0 3 1 1 0 0 0 0 0 | * * * 6 * * * * * | 1 0 0 2 0 0 | 2 0 1
... x.o3o.o o.x ...&#x ♦ 3 0 2 | 3 0 6 0 0 1 | 1 0 0 6 3 0 0 0 0 | 0 0 0 0 2 3 0 0 0 0 | * * * * 3 * * * * | 0 0 0 2 1 0 | 1 0 2
... xoo ... oox ...&#x ♦ 2 1 2 | 1 2 4 0 2 1 | 0 0 1 2 2 4 0 1 0 | 0 0 2 0 0 1 2 0 0 0 | * * * * * 18 * * * | 0 1 0 1 0 1 | 1 1 1
... x.o ... o.x3o.o&#x ♦ 2 0 3 | 1 0 6 0 0 3 | 0 0 0 3 6 0 0 0 1 | 0 0 0 0 0 3 0 2 0 0 | * * * * * * 3 * * | 0 0 0 0 1 2 | 0 1 2
... ... ... oox3ooo&#x ♦ 1 1 3 | 0 1 3 0 3 3 | 0 0 0 0 3 3 0 3 1 | 0 0 0 0 0 0 3 1 0 1 | * * * * * * * 6 * | 0 0 1 0 0 2 | 0 2 1
.xo ... ... .ox3.oo&#x ♦ 0 2 3 | 0 0 0 1 6 3 | 0 0 0 0 0 0 3 6 1 | 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * 1 | 0 0 3 0 0 0 | 0 3 0
-----------------------+-------+-------------+--------------------+-----------------------+--------------------+-------------+------
oxo xoo3ooo ... ...&#x ♦ 3 2 1 | 3 6 3 1 2 0 | 1 3 6 3 0 6 1 0 0 | 3 3 6 2 1 0 0 0 0 0 | 3 1 0 2 0 0 0 0 0 | 3 * * * * * | 2 0 0
oxo xoo ... oox ...&#x ♦ 2 2 2 | 1 4 4 1 4 1 | 0 2 2 2 2 8 2 2 0 | 4 1 4 0 0 1 4 0 1 0 | 2 0 2 0 0 2 0 0 0 | * 9 * * * * | 1 1 0
oxo ... ... oox3ooo&#x ♦ 1 2 3 | 0 2 3 1 6 3 | 0 1 0 0 3 6 3 6 1 | 3 0 0 0 0 0 6 1 3 2 | 0 0 3 0 0 0 0 2 1 | * * 3 * * * | 0 2 0
... xoo3ooo oox ...&#x ♦ 3 1 2 | 3 3 6 0 2 1 | 1 0 3 6 3 6 0 1 0 | 0 0 6 1 2 3 3 0 0 0 | 0 0 0 2 1 3 0 0 0 | * * * 6 * * | 1 0 1
... x.o3o.o o.x3o.o&#x ♦ 3 0 3 | 3 0 9 0 0 3 | 1 0 0 9 9 0 0 0 1 | 0 0 0 0 3 9 0 3 0 0 | 0 0 0 0 3 0 3 0 0 | * * * * 1 * | 0 0 2
... xoo ... oox3ooo&#x ♦ 2 1 3 | 1 2 6 0 3 3 | 0 0 1 3 6 6 0 3 1 | 0 0 3 0 0 3 6 2 0 1 | 0 0 0 0 0 3 1 2 0 | * * * * * 6 | 0 1 1
-----------------------+-------+-------------+--------------------+-----------------------+--------------------+-------------+------
oxo xoo3ooo oox ...&#x ♦ 3 2 2 | 3 6 6 1 4 1 | 1 3 6 6 3 12 2 2 0 | 6 3 12 2 2 3 6 0 1 0 | 6 1 3 4 1 6 0 0 0 | 2 3 0 2 0 0 | 3 * *
oxo xoo ... oox3ooo&#x ♦ 2 2 3 | 1 4 6 1 6 3 | 0 2 2 3 6 12 3 6 1 | 6 1 6 0 0 3 12 2 3 2 | 3 0 6 0 0 6 1 4 1 | 0 3 2 0 0 2 | * 3 *
... xoo3ooo oox3ooo&#x ♦ 3 1 3 | 3 3 9 0 3 3 | 1 0 3 9 9 9 0 3 1 | 0 0 9 1 3 9 9 3 0 1 | 0 0 0 3 3 9 3 3 0 | 0 0 0 3 1 3 | * * 2
xoo oxo3ooo3ooo oox&#x → height(1,2) = height(2,3) = sqrt(3/8) = 0.612372
height(1,3) = 1/sqrt(2) = 0.707107
( (line || perp line) || perp tet)
o.. o..3o..3o.. o.. | 2 * * ♦ 1 4 2 0 0 0 | 4 6 2 1 8 0 0 0 | 4 3 1 12 4 4 0 0 0 | 12 4 4 8 1 6 0 0 | 8 1 6 2 4 0 | 2 4 1
.o. .o.3.o.3.o. .o. | * 4 * ♦ 0 2 0 3 2 0 | 1 6 0 0 4 3 6 1 | 2 3 0 12 6 2 1 6 3 | 6 3 1 12 2 6 2 3 | 6 1 3 4 6 1 | 2 3 2
..o ..o3..o3..o ..o | * * 2 ♦ 0 0 2 0 4 1 | 0 0 1 2 8 0 6 4 | 4 0 1 12 0 8 0 4 6 | 6 0 4 8 0 12 1 4 | 4 0 6 2 8 1 | 1 4 2
-----------------------+-------+-------------+--------------------+--------------------+--------------------+-------------+------
x.. ... ... ... ... | 2 0 0 | 1 * * * * * ♦ 4 0 2 0 0 0 0 0 | 8 6 1 0 0 0 0 0 0 | 12 4 4 0 0 0 0 0 | 8 1 6 0 0 0 | 2 4 0
oo. oo.3oo.3oo. oo.&#x | 1 1 0 | * 8 * * * * ♦ 1 3 0 0 2 0 0 0 | 2 3 0 6 3 1 0 0 0 | 6 3 1 6 1 3 0 0 | 6 1 3 2 3 0 | 2 3 1
o.o o.o3o.o3o.o o.o&#x | 1 0 1 | * * 4 * * * ♦ 0 0 1 1 4 0 0 0 | 4 0 1 6 0 4 0 0 0 | 6 0 4 4 0 6 0 0 | 4 0 6 1 4 0 | 1 4 1
... .x. ... ... ... | 0 2 0 | * * * 6 * * ♦ 0 2 0 0 0 2 2 0 | 0 1 0 4 4 0 1 4 1 | 2 2 0 8 2 2 2 2 | 4 1 1 4 4 1 | 2 2 2
.oo .oo3.oo3.oo .oo&#x | 0 1 1 | * * * * 8 * ♦ 0 0 0 0 2 0 3 1 | 1 0 0 6 0 2 0 3 3 | 3 0 1 6 0 6 1 3 | 3 0 3 2 6 1 | 1 3 2
... ... ... ... ..x | 0 0 2 | * * * * * 1 ♦ 0 0 0 2 0 0 0 4 | 0 0 1 0 0 8 0 0 6 | 0 0 4 0 0 12 0 4 | 0 0 6 0 8 1 | 0 4 2
-----------------------+-------+-------------+--------------------+--------------------+--------------------+-------------+------
xo. ... ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | 4 * * * * * * * ♦ 2 4 0 0 0 0 0 0 0 | 6 3 1 0 0 0 0 0 | 6 1 3 0 0 0 | 2 3 0
... ox. ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 12 * * * * * * ♦ 0 1 0 2 2 0 0 0 0 | 2 2 0 2 1 1 0 0 | 4 1 1 2 2 0 | 2 2 1
x.o ... ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * 2 * * * * * ♦ 4 0 1 0 0 0 0 0 0 | 6 0 4 0 0 0 0 0 | 4 0 6 0 0 0 | 1 4 0
... ... ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * 2 * * * * ♦ 0 0 1 0 0 4 0 0 0 | 0 0 4 0 0 6 0 0 | 0 0 6 0 4 0 | 0 4 1
ooo ooo3ooo3ooo ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * 16 * * * ♦ 1 0 0 3 0 1 0 0 0 | 3 0 1 3 0 3 0 0 | 3 0 3 1 3 0 | 1 3 1
... .x.3.o. ... ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * 4 * * ♦ 0 0 0 0 2 0 1 2 0 | 0 1 0 4 2 0 2 1 | 2 1 0 4 2 1 | 2 1 2
... .xo ... ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * 12 * ♦ 0 0 0 2 0 0 0 2 1 | 1 0 0 4 0 2 1 2 | 2 0 1 2 4 1 | 1 2 2
... ... ... ... .ox&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * 4 ♦ 0 0 0 0 0 2 0 0 3 | 0 0 1 0 0 6 0 3 | 0 0 3 0 6 1 | 0 3 2
-----------------------+-------+-------------+--------------------+--------------------+--------------------+-------------+------
xoo ... ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 1 0 1 0 2 0 0 0 | 8 * * * * * * * * ♦ 3 0 1 0 0 0 0 0 | 3 0 3 0 0 0 | 1 3 0
xo. ox. ... ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 2 0 0 0 0 0 0 | * 6 * * * * * * * ♦ 2 2 0 0 0 0 0 0 | 4 1 1 0 0 0 | 2 2 0
x.o ... ... ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 2 2 0 0 0 0 | * * 1 * * * * * * ♦ 0 0 4 0 0 0 0 0 | 0 0 6 0 0 0 | 0 4 0
... oxo ... ... ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 1 0 0 2 0 1 0 | * * * 24 * * * * * ♦ 1 0 0 2 0 1 0 0 | 2 0 1 1 2 0 | 1 2 1
... ox.3oo. ... ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 0 0 1 0 0 | * * * * 8 * * * * ♦ 0 1 0 2 1 0 0 0 | 2 1 0 2 1 0 | 2 1 1
... ... ... ... oox&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 1 2 0 0 1 | * * * * * 8 * * * ♦ 0 0 1 0 0 3 0 0 | 0 0 3 0 3 0 | 0 3 1
... .x.3.o.3.o. ... ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 4 0 0 | * * * * * * 1 * * ♦ 0 0 0 0 2 0 2 0 | 0 1 0 4 0 1 | 2 0 2
... .xo3.oo ... ...&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 0 0 1 3 0 | * * * * * * * 8 * ♦ 0 0 0 2 0 0 1 1 | 1 0 0 2 2 1 | 1 1 2
... .xo ... ... .ox&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 0 2 2 | * * * * * * * * 6 ♦ 0 0 0 0 0 2 0 2 | 0 0 1 0 4 1 | 0 2 2
-----------------------+-------+-------------+--------------------+--------------------+--------------------+-------------+------
xoo oxo ... ... ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 2 2 1 0 4 0 1 0 | 2 1 0 2 0 0 0 0 0 | 12 * * * * * * * | 2 0 1 0 0 0 | 1 2 0
xo. ox.3oo. ... ...&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 3 6 0 0 0 1 0 0 | 0 3 0 0 2 0 0 0 0 | * 4 * * * * * * | 2 1 0 0 0 0 | 2 1 0
xoo ... ... ... oox&#x ♦ 2 1 2 | 1 2 4 0 2 1 | 1 0 2 2 4 0 0 1 | 2 0 1 0 0 2 0 0 0 | * * 4 * * * * * | 0 0 3 0 0 0 | 0 3 0
... oxo3ooo ... ...&#x ♦ 1 3 1 | 0 3 1 3 3 0 | 0 3 0 0 3 1 3 0 | 0 0 0 3 1 0 0 1 0 | * * * 16 * * * * | 1 0 0 1 1 0 | 1 1 1
... ox.3oo.3oo. ...&#x ♦ 1 4 0 | 0 4 0 6 0 0 | 0 6 0 0 0 4 0 0 | 0 0 0 0 4 0 1 0 0 | * * * * 2 * * * | 0 1 0 2 0 0 | 2 0 1
... oxo ... ... oox&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 1 0 1 4 0 2 2 | 0 0 0 2 0 2 0 0 1 | * * * * * 12 * * | 0 0 1 0 2 0 | 0 2 1
... .xo3.oo3.oo ...&#x ♦ 0 4 1 | 0 0 0 6 4 0 | 0 0 0 0 0 4 6 0 | 0 0 0 0 0 0 1 4 0 | * * * * * * 2 * | 0 0 0 2 0 1 | 1 0 2
... .xo3.oo ... .ox&#x ♦ 0 3 2 | 0 0 0 3 6 1 | 0 0 0 0 0 1 6 3 | 0 0 0 0 0 0 0 2 3 | * * * * * * * 4 | 0 0 0 0 2 1 | 0 1 2
-----------------------+-------+-------------+--------------------+--------------------+--------------------+-------------+------
xoo oxo3ooo ... ...&#x ♦ 2 3 1 | 1 6 2 3 3 0 | 3 6 1 0 6 1 3 0 | 3 3 0 6 2 0 0 1 0 | 3 1 0 2 0 0 0 0 | 8 * * * * * | 1 1 0
xo. ox.3oo.3oo. ...&#x ♦ 2 4 0 | 1 8 0 6 0 0 | 4 12 0 0 0 4 0 0 | 0 6 0 0 8 0 1 0 0 | 0 4 0 0 2 0 0 0 | * 1 * * * * | 2 0 0
xoo oxo ... ... oox&#x ♦ 2 2 2 | 1 4 4 1 4 1 | 2 2 2 2 8 0 2 2 | 4 1 1 4 0 4 0 0 1 | 2 0 2 0 0 2 0 0 | * * 6 * * * | 0 2 0
... oxo3ooo3ooo ...&#x ♦ 1 4 1 | 0 4 1 6 4 0 | 0 6 0 0 4 4 6 0 | 0 0 0 6 4 0 1 4 0 | 0 0 0 4 1 0 1 0 | * * * 4 * * | 1 0 1
... oxo3ooo ... oox&#x ♦ 1 3 2 | 0 3 2 3 6 1 | 0 3 0 1 6 1 6 3 | 0 0 0 6 1 3 0 2 3 | 0 0 0 2 0 3 0 1 | * * * * 8 * | 0 1 1
... .xo3.oo3.oo .ox&#x ♦ 0 4 2 | 0 0 0 6 8 1 | 0 0 0 0 0 4 12 4 | 0 0 0 0 0 0 1 8 6 | 0 0 0 0 0 0 2 4 | * * * * * 1 | 0 0 2
-----------------------+-------+-------------+--------------------+--------------------+--------------------+-------------+------
xoo oxo3ooo3ooo ...&#x ♦ 2 4 1 | 1 8 2 6 4 0 | 4 12 1 0 8 4 6 0 | 4 6 0 12 8 0 1 4 0 | 6 4 0 8 2 0 1 0 | 4 1 0 2 0 0 | 2 * *
xoo oxo3ooo ... oox&#x ♦ 2 3 2 | 1 6 4 3 6 1 | 3 6 2 2 12 1 6 3 | 6 3 1 12 2 6 0 2 3 | 6 1 3 4 0 6 0 1 | 2 0 3 0 2 0 | * 4 *
... oxo3ooo3ooo oox&#x ♦ 1 4 2 | 0 4 2 6 8 1 | 0 6 0 1 8 4 12 4 | 0 0 0 12 4 4 1 8 6 | 0 0 0 8 1 6 2 4 | 0 0 0 2 4 1 | * * 2
oxoo3oooo ooxo3oooo&#x → height(1,4) = 1
height(1,2) = height(1,3) = height(2,4) = height(3,4) = sqrt(2/3) = 0.816497
height(2,3) = 1/sqrt(3) = 0.577350
( pt || ( pt || ( {3} || ortho {3} )))
o...3o... o...3o... | 1 * * * ♦ 3 3 1 0 0 0 0 0 | 3 9 3 3 3 0 0 0 0 0 0 0 | 1 9 3 9 9 1 3 0 0 0 0 0 0 0 | 3 1 9 9 3 9 1 0 0 0 0 0 | 3 3 3 9 3 0 0 0 | 1 3 3 0
.o..3.o.. .o..3.o.. | * 3 * * ♦ 1 0 0 2 3 1 0 0 | 2 3 1 0 0 1 6 2 3 3 0 0 | 1 6 2 3 3 0 0 3 1 6 6 1 3 0 | 3 1 6 6 1 3 0 3 3 2 6 1 | 3 3 2 6 1 1 3 2 | 1 3 2 1
..o.3..o. ..o.3..o. | * * 3 * ♦ 0 1 0 0 3 0 2 1 | 0 3 0 2 1 0 3 0 6 3 1 2 | 0 3 0 6 3 1 2 1 0 6 3 3 6 1 | 1 0 6 3 3 6 1 2 1 3 6 3 | 2 1 3 6 3 1 2 3 | 1 2 3 1
...o3...o ...o3...o | * * * 1 ♦ 0 0 1 0 0 3 0 3 | 0 0 3 0 3 0 0 3 0 9 0 3 | 0 0 3 0 9 0 3 0 1 0 9 0 9 1 | 0 1 0 9 0 9 1 0 3 0 9 3 | 0 3 0 9 3 0 3 3 | 0 3 3 1
-----------------------+---------+-----------------+-------------------------+-----------------------------+-------------------------+-----------------+--------
oo..3oo.. oo..3oo..&#x | 1 1 0 0 | 3 * * * * * * * ♦ 2 3 1 0 0 0 0 0 0 0 0 0 | 1 6 2 3 3 0 0 0 0 0 0 0 0 0 | 3 1 6 6 1 3 0 0 0 0 0 0 | 3 3 2 6 1 0 0 0 | 1 3 2 0
o.o.3o.o. o.o.3o.o.&#x | 1 0 1 0 | * 3 * * * * * * ♦ 0 3 0 2 1 0 0 0 0 0 0 0 | 0 3 0 6 3 1 2 0 0 0 0 0 0 0 | 1 0 6 3 3 6 1 0 0 0 0 0 | 2 1 3 6 3 0 0 0 | 1 2 3 0
o..o3o..o o..o3o..o&#x | 1 0 0 1 | * * 1 * * * * * ♦ 0 0 3 0 3 0 0 0 0 0 0 0 | 0 0 3 0 9 0 3 0 0 0 0 0 0 0 | 0 1 0 9 0 9 1 0 0 0 0 0 | 0 3 0 9 3 0 0 0 | 0 3 3 0
.x.. .... .... .... | 0 2 0 0 | * * * 3 * * * * ♦ 1 0 0 0 0 1 3 1 0 0 0 0 | 1 3 1 0 0 0 0 3 1 3 3 0 0 0 | 3 1 3 3 0 0 0 3 3 1 3 0 | 3 3 1 3 0 1 3 1 | 1 3 1 1
.oo.3.oo. .oo.3.oo.&#x | 0 1 1 0 | * * * * 9 * * * ♦ 0 1 0 0 0 0 2 0 2 1 0 0 | 0 2 0 2 1 0 0 1 0 4 2 1 2 0 | 1 0 4 2 1 2 0 2 1 2 4 1 | 2 1 2 4 1 1 2 2 | 1 2 2 1
.o.o3.o.o .o.o3.o.o&#x | 0 1 0 1 | * * * * * 3 * * ♦ 0 0 1 0 0 0 0 2 0 3 0 0 | 0 0 2 0 3 0 0 0 1 0 6 0 3 0 | 0 1 0 6 0 3 0 0 3 0 6 1 | 0 3 0 6 1 0 3 2 | 0 3 2 1
.... .... ..x. .... | 0 0 2 0 | * * * * * * 3 * ♦ 0 0 0 1 0 0 0 0 3 0 1 1 | 0 0 0 3 0 1 1 0 0 3 0 3 3 1 | 0 0 3 0 3 3 1 1 0 3 3 3 | 1 0 3 3 3 1 1 3 | 1 1 3 1
..oo3..oo ..oo3..oo&#x | 0 0 1 1 | * * * * * * * 3 ♦ 0 0 0 0 1 0 0 0 0 3 0 2 | 0 0 0 0 3 0 2 0 0 0 3 0 6 1 | 0 0 0 3 0 6 1 0 1 0 6 3 | 0 1 0 6 3 0 2 3 | 0 2 3 1
-----------------------+---------+-----------------+-------------------------+-----------------------------+-------------------------+-----------------+--------
ox.. .... .... ....&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 | 3 * * * * * * * * * * * ♦ 1 3 1 0 0 0 0 0 0 0 0 0 0 0 | 3 1 3 3 0 0 0 0 0 0 0 0 | 3 3 1 3 0 0 0 0 | 1 3 1 0
ooo.3ooo. ooo.3ooo.&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 | * 9 * * * * * * * * * * ♦ 0 2 0 2 1 0 0 0 0 0 0 0 0 0 | 1 0 4 2 1 2 0 0 0 0 0 0 | 2 1 2 4 1 0 0 0 | 1 2 2 0
oo.o3oo.o oo.o3oo.o&#x | 1 1 0 1 | 1 0 1 0 0 1 0 0 | * * 3 * * * * * * * * * ♦ 0 0 2 0 3 0 0 0 0 0 0 0 0 0 | 0 1 0 6 0 3 0 0 0 0 0 0 | 0 3 0 6 1 0 0 0 | 0 3 2 0
.... .... o.x. ....&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 | * * * 3 * * * * * * * * ♦ 0 0 0 3 0 1 1 0 0 0 0 0 0 0 | 0 0 3 0 3 3 1 0 0 0 0 0 | 1 0 3 3 3 0 0 0 | 1 1 3 0
o.oo3o.oo o.oo3o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 | * * * * 3 * * * * * * * ♦ 0 0 0 0 3 0 2 0 0 0 0 0 0 0 | 0 0 0 3 0 6 1 0 0 0 0 0 | 0 1 0 6 3 0 0 0 | 0 2 3 0
.x..3.o.. .... .... | 0 3 0 0 | 0 0 0 3 0 0 0 0 | * * * * * 1 * * * * * * ♦ 1 0 0 0 0 0 0 3 1 0 0 0 0 0 | 3 1 0 0 0 0 0 3 3 0 0 0 | 3 3 0 0 0 1 3 0 | 1 3 0 1
.xo. .... .... ....&#x | 0 2 1 0 | 0 0 0 1 2 0 0 0 | * * * * * * 9 * * * * * ♦ 0 1 0 0 0 0 0 1 0 2 1 0 0 0 | 1 0 2 1 0 0 0 2 1 1 2 0 | 2 1 1 2 0 1 2 1 | 1 2 1 1
.x.o .... .... ....&#x | 0 2 0 1 | 0 0 0 1 0 2 0 0 | * * * * * * * 3 * * * * ♦ 0 0 1 0 0 0 0 0 1 0 3 0 0 0 | 0 1 0 3 0 0 0 0 3 0 3 0 | 0 3 0 3 0 0 3 1 | 0 3 1 1
.... .... .ox. ....&#x | 0 1 2 0 | 0 0 0 0 2 0 1 0 | * * * * * * * * 9 * * * ♦ 0 0 0 1 0 0 0 0 0 2 0 1 1 0 | 0 0 2 0 1 1 0 1 0 2 2 1 | 1 0 2 2 1 1 1 2 | 1 1 2 1
.ooo3.ooo .ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 | * * * * * * * * * 9 * * ♦ 0 0 0 0 1 0 0 0 0 0 2 0 2 0 | 0 0 0 2 0 2 0 0 1 0 4 1 | 0 1 0 4 1 0 2 2 | 0 2 2 1
.... .... ..x.3..o. | 0 0 3 0 | 0 0 0 0 0 0 3 0 | * * * * * * * * * * 1 * ♦ 0 0 0 0 0 1 0 0 0 0 0 3 0 1 | 0 0 0 0 3 0 1 0 0 3 0 3 | 0 0 3 0 3 1 0 3 | 1 0 3 1
.... .... ..xo ....&#x | 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * * * * * * * 3 ♦ 0 0 0 0 0 0 1 0 0 0 0 0 3 1 | 0 0 0 0 0 3 1 0 0 0 3 3 | 0 0 0 3 3 0 1 3 | 0 1 3 1
-----------------------+---------+-----------------+-------------------------+-----------------------------+-------------------------+-----------------+--------
ox..3oo.. .... ....&#x ♦ 1 3 0 0 | 3 0 0 3 0 0 0 0 | 3 0 0 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * ♦ 3 1 0 0 0 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 | 1 3 0 0
oxo. .... .... ....&#x ♦ 1 2 1 0 | 2 1 0 1 2 0 0 0 | 1 2 0 0 0 0 1 0 0 0 0 0 | * 9 * * * * * * * * * * * * ♦ 1 0 2 1 0 0 0 0 0 0 0 0 | 2 1 1 2 0 0 0 0 | 1 2 1 0
ox.o .... .... ....&#x ♦ 1 2 0 1 | 2 0 1 1 0 2 0 0 | 1 0 2 0 0 0 0 1 0 0 0 0 | * * 3 * * * * * * * * * * * ♦ 0 1 0 3 0 0 0 0 0 0 0 0 | 0 3 0 3 0 0 0 0 | 0 3 1 0
.... .... oox. ....&#x ♦ 1 1 2 0 | 1 2 0 0 2 0 1 0 | 0 2 0 1 0 0 0 0 1 0 0 0 | * * * 9 * * * * * * * * * * ♦ 0 0 2 0 1 1 0 0 0 0 0 0 | 1 0 2 2 1 0 0 0 | 1 1 2 0
oooo3oooo oooo3oooo&#x ♦ 1 1 1 1 | 1 1 1 0 1 1 0 1 | 0 1 1 0 1 0 0 0 0 1 0 0 | * * * * 9 * * * * * * * * * ♦ 0 0 0 2 0 2 0 0 0 0 0 0 | 0 1 0 4 1 0 0 0 | 0 2 2 0
.... .... o.x.3o.o.&#x ♦ 1 0 3 0 | 0 3 0 0 0 0 3 0 | 0 0 0 3 0 0 0 0 0 0 1 0 | * * * * * 1 * * * * * * * * ♦ 0 0 0 0 3 0 1 0 0 0 0 0 | 0 0 3 0 3 0 0 0 | 1 0 3 0
.... .... o.xo ....&#x ♦ 1 0 2 1 | 0 2 1 0 0 0 1 2 | 0 0 0 1 2 0 0 0 0 0 0 1 | * * * * * * 3 * * * * * * * ♦ 0 0 0 0 0 3 1 0 0 0 0 0 | 0 0 0 3 3 0 0 0 | 0 1 3 0
.xo.3.oo. .... ....&#x ♦ 0 3 1 0 | 0 0 0 3 3 0 0 0 | 0 0 0 0 0 1 3 0 0 0 0 0 | * * * * * * * 3 * * * * * * ♦ 1 0 0 0 0 0 0 2 1 0 0 0 | 2 1 0 0 0 1 2 0 | 1 2 0 1
.x.o3.o.o .... ....&#x ♦ 0 3 0 1 | 0 0 0 3 0 3 0 0 | 0 0 0 0 0 1 0 3 0 0 0 0 | * * * * * * * * 1 * * * * * ♦ 0 1 0 0 0 0 0 0 3 0 0 0 | 0 3 0 0 0 0 3 0 | 0 3 0 1
.xo. .... .ox. ....&#x ♦ 0 2 2 0 | 0 0 0 1 4 0 1 0 | 0 0 0 0 0 0 2 0 2 0 0 0 | * * * * * * * * * 9 * * * * ♦ 0 0 1 0 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 1 1
.xoo .... .... ....&#x ♦ 0 2 1 1 | 0 0 0 1 2 2 0 1 | 0 0 0 0 0 0 1 1 0 2 0 0 | * * * * * * * * * * 9 * * * ♦ 0 0 0 1 0 0 0 0 1 0 2 0 | 0 1 0 2 0 0 2 1 | 0 2 1 1
.... .... .ox.3.oo.&#x ♦ 0 1 3 0 | 0 0 0 0 3 0 3 0 | 0 0 0 0 0 0 0 0 3 0 1 0 | * * * * * * * * * * * 3 * * ♦ 0 0 0 0 1 0 0 0 0 2 0 1 | 0 0 2 0 1 1 0 2 | 1 0 2 1
.... .... .oxo ....&#x ♦ 0 1 2 1 | 0 0 0 0 2 1 1 2 | 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * 9 * ♦ 0 0 0 0 0 1 0 0 0 0 2 1 | 0 0 0 2 1 0 1 2 | 0 1 2 1
.... .... ..xo3..oo&#x ♦ 0 0 3 1 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 1 3 | * * * * * * * * * * * * * 1 ♦ 0 0 0 0 0 0 1 0 0 0 0 3 | 0 0 0 0 3 0 0 3 | 0 0 3 1
-----------------------+---------+-----------------+-------------------------+-----------------------------+-------------------------+-----------------+--------
oxo.3ooo. .... ....&#x ♦ 1 3 1 0 | 3 1 0 3 3 0 0 0 | 3 3 0 0 0 1 3 0 0 0 0 0 | 1 3 0 0 0 0 0 1 0 0 0 0 0 0 | 3 * * * * * * * * * * * | 2 1 0 0 0 0 0 0 | 1 2 0 0
ox.o3oo.o .... ....&#x ♦ 1 3 0 1 | 3 0 1 3 0 3 0 0 | 3 0 3 0 0 1 0 3 0 0 0 0 | 1 0 3 0 0 0 0 0 1 0 0 0 0 0 | * 1 * * * * * * * * * * | 0 3 0 0 0 0 0 0 | 0 3 0 0
oxo. .... oox. ....&#x ♦ 1 2 2 0 | 2 2 0 1 4 0 1 0 | 1 4 0 1 0 0 2 0 2 0 0 0 | 0 2 0 2 0 0 0 0 0 1 0 0 0 0 | * * 9 * * * * * * * * * | 1 0 1 1 0 0 0 0 | 1 1 1 0
oxoo .... .... ....&#x ♦ 1 2 1 1 | 2 1 1 1 2 2 0 1 | 1 2 2 0 1 0 1 1 0 2 0 0 | 0 1 1 0 2 0 0 0 0 0 1 0 0 0 | * * * 9 * * * * * * * * | 0 1 0 2 0 0 0 0 | 0 2 1 0
.... .... oox.3ooo.&#x ♦ 1 1 3 0 | 1 3 0 0 3 0 3 0 | 0 3 0 3 0 0 0 0 3 0 1 0 | 0 0 0 3 0 1 0 0 0 0 0 1 0 0 | * * * * 3 * * * * * * * | 0 0 2 0 1 0 0 0 | 1 0 2 0
.... .... ooxo ....&#x ♦ 1 1 2 1 | 1 2 1 0 2 1 1 2 | 0 2 1 1 2 0 0 0 1 2 0 1 | 0 0 0 1 2 0 1 0 0 0 0 0 1 0 | * * * * * 9 * * * * * * | 0 0 0 2 1 0 0 0 | 0 1 2 0
.... .... o.xo3o.oo&#x ♦ 1 0 3 1 | 0 3 1 0 0 0 3 3 | 0 0 0 3 3 0 0 0 0 0 1 3 | 0 0 0 0 0 1 3 0 0 0 0 0 0 1 | * * * * * * 1 * * * * * | 0 0 0 0 3 0 0 0 | 0 0 3 0
.xo.3.oo. .ox. ....&#x ♦ 0 3 2 0 | 0 0 0 3 6 0 1 0 | 0 0 0 0 0 1 6 0 3 0 0 0 | 0 0 0 0 0 0 0 2 0 3 0 0 0 0 | * * * * * * * 3 * * * * | 1 0 0 0 0 1 1 0 | 1 1 0 1
.xoo3.ooo .... ....&#x ♦ 0 3 1 1 | 0 0 0 3 3 3 0 1 | 0 0 0 0 0 1 3 3 0 3 0 0 | 0 0 0 0 0 0 0 1 1 0 3 0 0 0 | * * * * * * * * 3 * * * | 0 1 0 0 0 0 2 0 | 0 2 0 1
.xo. .... .ox.3.oo.&#x ♦ 0 2 3 0 | 0 0 0 1 6 0 3 0 | 0 0 0 0 0 0 3 0 6 0 1 0 | 0 0 0 0 0 0 0 0 0 3 0 2 0 0 | * * * * * * * * * 3 * * | 0 0 1 0 0 1 0 1 | 1 0 1 1
.xoo .... .oxo ....&#x ♦ 0 2 2 1 | 0 0 0 1 4 2 1 2 | 0 0 0 0 0 0 2 1 2 4 0 1 | 0 0 0 0 0 0 0 0 0 1 2 0 2 0 | * * * * * * * * * * 9 * | 0 0 0 1 0 0 1 1 | 0 1 1 1
.... .... .oxo3.ooo&#x ♦ 0 1 3 1 | 0 0 0 0 3 1 3 3 | 0 0 0 0 0 0 0 0 3 3 1 3 | 0 0 0 0 0 0 0 0 0 0 0 1 3 1 | * * * * * * * * * * * 3 | 0 0 0 0 1 0 0 2 | 0 0 2 1
-----------------------+---------+-----------------+-------------------------+-----------------------------+-------------------------+-----------------+--------
oxo.3ooo. oox. ....&#x ♦ 1 3 2 0 | 3 2 0 3 6 0 1 0 | 3 6 0 1 0 1 6 0 3 0 0 0 | 1 6 0 3 0 0 0 2 0 3 0 0 0 0 | 2 0 3 0 0 0 0 1 0 0 0 0 | 3 * * * * * * * | 1 1 0 0
oxoo3oooo .... ....&#x ♦ 1 3 1 1 | 3 1 1 3 3 3 0 1 | 3 3 3 0 1 1 3 3 0 3 0 0 | 1 3 3 0 3 0 0 1 1 0 3 0 0 0 | 1 1 0 3 0 0 0 0 1 0 0 0 | * 3 * * * * * * | 0 2 0 0
oxo. .... oox.3ooo.&#x ♦ 1 2 3 0 | 2 3 0 1 6 0 3 0 | 1 6 0 3 0 0 3 0 6 0 1 0 | 0 3 0 6 0 1 0 0 0 3 0 2 0 0 | 0 0 3 0 2 0 0 0 0 1 0 0 | * * 3 * * * * * | 1 0 1 0
oxoo .... ooxo ....&#x ♦ 1 2 2 1 | 2 2 1 1 4 2 1 2 | 1 4 2 1 2 0 2 1 2 4 0 1 | 0 2 1 2 4 0 1 0 0 1 2 0 2 0 | 0 0 1 2 0 2 0 0 0 0 1 0 | * * * 9 * * * * | 0 1 1 0
.... .... ooxo3oooo&#x ♦ 1 1 3 1 | 1 3 1 0 3 1 3 3 | 0 3 1 3 3 0 0 0 3 3 1 3 | 0 0 0 3 3 1 3 0 0 0 0 1 3 1 | 0 0 0 0 1 3 1 0 0 0 0 1 | * * * * 3 * * * | 0 0 2 0
.xo.3.oo. .ox.3.oo.&#x ♦ 0 3 3 0 | 0 0 0 3 9 0 3 0 | 0 0 0 0 0 1 9 0 9 0 1 0 | 0 0 0 0 0 0 0 3 0 9 0 3 0 0 | 0 0 0 0 0 0 0 3 0 3 0 0 | * * * * * 1 * * | 1 0 0 1
.xoo3.ooo .oxo ....&#x ♦ 0 3 2 1 | 0 0 0 3 6 3 1 2 | 0 0 0 0 0 1 6 3 3 6 0 1 | 0 0 0 0 0 0 0 2 1 3 6 0 3 0 | 0 0 0 0 0 0 0 1 2 0 3 0 | * * * * * * 3 * | 0 1 0 1
.xoo .... .oxo3.ooo&#x ♦ 0 2 3 1 | 0 0 0 1 6 2 3 3 | 0 0 0 0 0 0 3 1 6 6 1 3 | 0 0 0 0 0 0 0 0 0 3 3 2 6 1 | 0 0 0 0 0 0 0 0 0 1 3 2 | * * * * * * * 3 | 0 0 1 1
-----------------------+---------+-----------------+-------------------------+-----------------------------+-------------------------+-----------------+--------
oxo.3ooo. oox.3ooo.&#x ♦ 1 3 3 0 | 3 3 0 3 9 0 3 0 | 3 9 0 3 0 1 9 0 9 0 1 0 | 1 9 0 9 0 1 0 3 0 9 0 3 0 0 | 3 0 9 0 3 0 0 3 0 3 0 0 | 3 0 3 0 0 1 0 0 | 1 * * *
oxoo3oooo ooxo ....&#x ♦ 1 3 2 1 | 3 2 1 3 6 3 1 2 | 3 6 3 1 2 1 6 3 3 6 0 1 | 1 6 3 3 6 0 1 2 1 3 6 0 3 0 | 2 1 3 6 0 3 0 1 2 0 3 0 | 1 2 0 3 0 0 1 0 | * 3 * *
oxoo .... ooxo3oooo&#x ♦ 1 2 3 1 | 2 3 1 1 6 2 3 3 | 1 6 2 3 3 0 3 1 6 6 1 3 | 0 3 1 6 6 1 3 0 0 3 3 2 6 1 | 0 0 3 3 2 6 1 0 0 1 3 2 | 0 0 1 3 2 0 0 1 | * * 3 *
.xoo3.ooo .oxo3.ooo&#x ♦ 0 3 3 1 | 0 0 0 3 9 3 3 3 | 0 0 0 0 0 1 9 3 9 9 1 3 | 0 0 0 0 0 0 0 3 1 9 9 3 9 1 | 0 0 0 0 0 0 0 3 3 3 9 3 | 0 0 0 0 0 1 3 3 | * * * 1