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Acronym
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soxeb
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|
Name
|
small exiated bi-enneazetton,
heptellated enneazetton,
expanded enneazetton,
lattice A8 contact polytope (span of its roots),
equatorial cross-section of rene-first riv
|
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Circumradius
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1
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Inradius
wrt. oca
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3/4 = 0.75
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Inradius
wrt. hopip
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3/sqrt(28) = 0.566947
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Inradius
wrt. trahix
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1/2 = 0.5
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Inradius
wrt. tetpen
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3/sqrt(40) = 0.474342
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Lace city
in approx. ASCII-art
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o h -- o3o3o3o3o3o3x (oca)
H S h -- x3o3o3o3o3o3x (suph)
H o -- x3o3o3o3o3o3o (dual oca)
where:
o - o3o3o3o3o3o (point)
h - x3o3o3o3o3o (hop)
S - x3o3o3o3o3x (staf)
H - o3o3o3o3o3x (dual hop)
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Volume
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429/7168 = 0.059849
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Face vector
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72, 504, 1764, 3780, 5208, 4536, 2286, 510
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Confer
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- more general:
-
xPo3o...o3oPxQ*a
- uniform relative:
-
fy
- related segmentozetta:
-
ocasuph
- general polytopal classes:
-
Wythoffian polyzetta
segmentozetta
fundamental lace prisms
- analogs:
-
maximal epanded simplex eSn
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External
links
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Incidence matrix according to Dynkin symbol
x3o3o3o3o3o3o3x
. . . . . . . . | 72 | 7 7 | 21 42 21 | 35 105 105 35 | 35 140 210 140 35 | 21 105 210 210 105 21 | 7 42 105 140 105 42 7 | 1 7 21 35 35 21 7 1
----------------+----+---------+-------------+-------------------+------------------------+---------------------------+---------------------------+------------------------
x . . . . . . . | 2 | 252 * | 6 6 0 | 15 30 15 0 | 20 60 60 20 0 | 15 60 90 60 15 0 | 6 30 60 60 30 6 0 | 1 6 15 20 15 6 1 0
. . . . . . . x | 2 | * 252 | 0 6 6 | 0 15 30 15 | 0 20 60 60 20 | 0 15 60 90 60 15 | 0 6 30 60 60 30 6 | 0 1 6 15 20 15 6 1
----------------+----+---------+-------------+-------------------+------------------------+---------------------------+---------------------------+------------------------
x3o . . . . . . | 3 | 3 0 | 504 * * | 5 5 0 0 | 10 20 10 0 0 | 10 30 30 10 0 0 | 5 20 30 20 5 0 0 | 1 5 10 10 5 1 0 0
x . . . . . . x | 4 | 2 2 | * 756 * | 0 5 5 0 | 0 10 20 10 0 | 0 10 30 30 10 0 | 0 5 20 30 20 5 0 | 0 1 5 10 10 5 1 0
. . . . . . o3x | 3 | 0 3 | * * 504 | 0 0 5 5 | 0 0 10 20 10 | 0 0 10 30 30 10 | 0 0 5 20 30 20 5 | 0 0 1 5 10 10 5 1
----------------+----+---------+-------------+-------------------+------------------------+---------------------------+---------------------------+------------------------
x3o3o . . . . . ♦ 4 | 6 0 | 4 0 0 | 630 * * * | 4 4 0 0 0 | 6 12 6 0 0 0 | 4 12 12 4 0 0 0 | 1 4 6 4 1 0 0 0
x3o . . . . . x ♦ 6 | 6 3 | 2 3 0 | * 1260 * * | 0 4 4 0 0 | 0 6 12 6 0 0 | 0 4 12 12 4 0 0 | 0 1 4 6 4 1 0 0
x . . . . . o3x ♦ 6 | 3 6 | 0 3 2 | * * 1260 * | 0 0 4 4 0 | 0 0 6 12 6 0 | 0 0 4 12 12 4 0 | 0 0 1 4 6 4 1 0
. . . . . o3o3x ♦ 4 | 0 6 | 0 0 4 | * * * 630 | 0 0 0 4 4 | 0 0 0 6 12 6 | 0 0 0 4 12 12 4 | 0 0 0 1 4 6 4 1
----------------+----+---------+-------------+-------------------+------------------------+---------------------------+---------------------------+------------------------
x3o3o3o . . . . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 0 | 504 * * * * | 3 3 0 0 0 0 | 3 6 3 0 0 0 0 | 1 3 3 1 0 0 0 0
x3o3o . . . . x ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | * 1260 * * * | 0 3 3 0 0 0 | 0 3 6 3 0 0 0 | 0 1 3 3 1 0 0 0
x3o . . . . o3x ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 | * * 1680 * * | 0 0 3 3 0 0 | 0 0 3 6 3 0 0 | 0 0 1 3 3 1 0 0
x . . . . o3o3x ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 | * * * 1260 * | 0 0 0 3 3 0 | 0 0 0 3 6 3 0 | 0 0 0 1 3 3 1 0
. . . . o3o3o3x ♦ 5 | 0 10 | 0 0 10 | 0 0 0 5 | * * * * 504 | 0 0 0 0 3 3 | 0 0 0 0 3 6 3 | 0 0 0 0 1 3 3 1
----------------+----+---------+-------------+-------------------+------------------------+---------------------------+---------------------------+------------------------
x3o3o3o3o . . . ♦ 6 | 15 0 | 20 0 0 | 15 0 0 0 | 6 0 0 0 0 | 252 * * * * * | 2 2 0 0 0 0 0 | 1 2 1 0 0 0 0 0
x3o3o3o . . . x ♦ 10 | 20 5 | 20 10 0 | 10 10 0 0 | 2 5 0 0 0 | * 756 * * * * | 0 2 2 0 0 0 0 | 0 1 2 1 0 0 0 0
x3o3o . . . o3x ♦ 12 | 18 12 | 12 18 4 | 3 12 6 0 | 0 3 4 0 0 | * * 1260 * * * | 0 0 2 2 0 0 0 | 0 0 1 2 1 0 0 0
x3o . . . o3o3x ♦ 12 | 12 18 | 4 18 12 | 0 6 12 3 | 0 0 4 3 0 | * * * 1260 * * | 0 0 0 2 2 0 0 | 0 0 0 1 2 1 0 0
x . . . o3o3o3x ♦ 10 | 5 20 | 0 10 20 | 0 0 10 10 | 0 0 0 5 2 | * * * * 756 * | 0 0 0 0 2 2 0 | 0 0 0 0 1 2 1 0
. . . o3o3o3o3x ♦ 6 | 0 15 | 0 0 20 | 0 0 0 15 | 0 0 0 0 6 | * * * * * 252 | 0 0 0 0 0 2 2 | 0 0 0 0 0 1 2 1
----------------+----+---------+-------------+-------------------+------------------------+---------------------------+---------------------------+------------------------
x3o3o3o3o3o . . ♦ 7 | 21 0 | 35 0 0 | 35 0 0 0 | 21 0 0 0 0 | 7 0 0 0 0 0 | 72 * * * * * * | 1 1 0 0 0 0 0 0
x3o3o3o3o . . x ♦ 12 | 30 6 | 40 15 0 | 30 20 0 0 | 12 15 0 0 0 | 2 6 0 0 0 0 | * 252 * * * * * | 0 1 1 0 0 0 0 0
x3o3o3o . . o3x ♦ 15 | 30 15 | 30 30 5 | 15 30 10 0 | 3 15 10 0 0 | 0 3 5 0 0 0 | * * 504 * * * * | 0 0 1 1 0 0 0 0
x3o3o . . o3o3x ♦ 16 | 24 24 | 16 36 16 | 4 24 24 4 | 0 6 16 6 0 | 0 0 4 4 0 0 | * * * 630 * * * | 0 0 0 1 1 0 0 0
x3o . . o3o3o3x ♦ 15 | 15 30 | 5 30 30 | 0 10 30 15 | 0 0 10 15 3 | 0 0 0 5 3 0 | * * * * 504 * * | 0 0 0 0 1 1 0 0
x . . o3o3o3o3x ♦ 12 | 6 30 | 0 15 40 | 0 0 20 30 | 0 0 0 15 12 | 0 0 0 0 6 2 | * * * * * 252 * | 0 0 0 0 0 1 1 0
. . o3o3o3o3o3x ♦ 7 | 0 21 | 0 0 35 | 0 0 0 35 | 0 0 0 0 21 | 0 0 0 0 0 7 | * * * * * * 72 | 0 0 0 0 0 0 1 1
----------------+----+---------+-------------+-------------------+------------------------+---------------------------+---------------------------+------------------------
x3o3o3o3o3o3o . ♦ 8 | 28 0 | 56 0 0 | 70 0 0 0 | 56 0 0 0 0 | 28 0 0 0 0 0 | 8 0 0 0 0 0 0 | 9 * * * * * * *
x3o3o3o3o3o . x ♦ 14 | 42 7 | 70 21 0 | 70 35 0 0 | 42 35 0 0 0 | 14 21 0 0 0 0 | 2 7 0 0 0 0 0 | * 36 * * * * * *
x3o3o3o3o . o3x ♦ 18 | 45 18 | 60 45 6 | 45 60 15 0 | 18 45 20 0 0 | 3 18 15 0 0 0 | 0 3 6 0 0 0 0 | * * 84 * * * * *
x3o3o3o . o3o3x ♦ 20 | 40 30 | 40 60 20 | 20 60 40 5 | 4 30 40 10 0 | 0 6 20 10 0 0 | 0 0 4 5 0 0 0 | * * * 126 * * * *
x3o3o . o3o3o3x ♦ 20 | 30 40 | 20 60 40 | 5 40 60 20 | 0 10 40 30 4 | 0 0 10 20 6 0 | 0 0 0 5 4 0 0 | * * * * 126 * * *
x3o . o3o3o3o3x ♦ 18 | 18 45 | 6 45 60 | 0 15 60 45 | 0 0 20 45 18 | 0 0 0 15 18 3 | 0 0 0 0 6 3 0 | * * * * * 84 * *
x . o3o3o3o3o3x ♦ 14 | 7 42 | 0 21 70 | 0 0 35 70 | 0 0 0 35 42 | 0 0 0 0 21 14 | 0 0 0 0 0 7 2 | * * * * * * 36 *
. o3o3o3o3o3o3x ♦ 8 | 0 28 | 0 0 56 | 0 0 0 70 | 0 0 0 0 56 | 0 0 0 0 0 28 | 0 0 0 0 0 0 8 | * * * * * * * 9
or
. . . . . . . . & | 72 | 14 | 42 42 | 70 210 | 70 280 210 | 42 210 420 | 14 84 210 140 | 2 14 42 70
-------------------+----+-----+----------+-----------+----------------+---------------+------------------+--------------
x . . . . . . . & | 2 | 504 | 6 6 | 15 45 | 20 80 60 | 15 75 150 | 6 36 90 60 | 1 7 21 35
-------------------+----+-----+----------+-----------+----------------+---------------+------------------+--------------
x3o . . . . . . & | 3 | 3 | 1008 * | 5 5 | 10 20 10 | 10 30 40 | 5 20 35 20 | 1 5 11 15
x . . . . . . x | 4 | 4 | * 756 | 0 10 | 0 20 20 | 0 20 60 | 0 10 40 30 | 0 2 10 20
-------------------+----+-----+----------+-----------+----------------+---------------+------------------+--------------
x3o3o . . . . . & ♦ 4 | 6 | 4 0 | 1260 * | 4 4 0 | 6 12 6 | 4 12 12 4 | 1 4 6 5
x3o . . . . . x & ♦ 6 | 9 | 2 3 | * 2520 | 0 4 4 | 0 6 18 | 0 4 12 16 | 0 1 5 10
-------------------+----+-----+----------+-----------+----------------+---------------+------------------+--------------
x3o3o3o . . . . & ♦ 5 | 10 | 10 0 | 5 0 | 1008 * * | 3 3 0 | 3 6 3 0 | 1 3 3 1
x3o3o . . . . x & ♦ 8 | 16 | 8 6 | 2 4 | * 2520 * | 0 3 3 | 0 3 6 3 | 0 1 3 4
x3o . . . . o3x ♦ 9 | 18 | 6 9 | 0 6 | * * 1680 | 0 0 6 | 0 0 3 9 | 0 0 2 6
-------------------+----+-----+----------+-----------+----------------+---------------+------------------+--------------
x3o3o3o3o . . . & ♦ 6 | 15 | 20 0 | 15 0 | 6 0 0 | 504 * * | 2 2 0 0 | 1 2 1 0
x3o3o3o . . . x & ♦ 10 | 25 | 20 10 | 10 10 | 2 5 0 | * 1512 * | 0 2 2 0 | 0 1 2 1
x3o3o . . . o3x & ♦ 12 | 30 | 16 18 | 3 18 | 0 3 4 | * * 2520 | 0 0 2 2 | 0 0 1 3
-------------------+----+-----+----------+-----------+----------------+---------------+------------------+--------------
x3o3o3o3o3o . . & ♦ 7 | 21 | 35 0 | 35 0 | 21 0 0 | 7 0 0 | 144 * * * | 1 1 0 0
x3o3o3o3o . . x & ♦ 12 | 36 | 40 15 | 30 20 | 12 15 0 | 2 6 0 | * 504 * * | 0 1 1 0
x3o3o3o . . o3x & ♦ 15 | 45 | 35 30 | 15 40 | 3 15 10 | 0 3 5 | * * 1008 * | 0 0 1 1
x3o3o . . o3o3x ♦ 16 | 48 | 32 36 | 8 48 | 0 12 16 | 0 0 8 | * * * 630 | 0 0 0 2
-------------------+----+-----+----------+-----------+----------------+---------------+------------------+--------------
x3o3o3o3o3o3o . & ♦ 8 | 28 | 56 0 | 70 0 | 56 0 0 | 28 0 0 | 8 0 0 0 | 18 * * *
x3o3o3o3o3o . x & ♦ 14 | 49 | 70 21 | 70 35 | 42 35 0 | 14 21 0 | 2 7 0 0 | * 72 * *
x3o3o3o3o . o3x & ♦ 18 | 63 | 66 45 | 45 75 | 18 45 20 | 3 18 15 | 0 3 6 0 | * * 168 *
x3o3o3o . o3o3x & ♦ 20 | 70 | 60 60 | 25 100 | 4 40 40 | 0 6 30 | 0 0 4 5 | * * * 252
xxo3ooo3ooo3ooo3ooo3ooo3oxx&#xt → both heights = 3/4
(oca || pseudo suph || dual oca)
...