Acronym | he (old: ache) |
Name |
hexadecaexon, trirectified octaexon, equatorial cross-section of (vertex first) 1/q-octo, Gosset polytope 03,3 |
Circumradius | 1 |
Inradius | 1/sqrt(7) = 0.377964 |
Lace city in approx. ASCII-art |
R D R = o3x3o3o3o (rix) D = o3o3x3o3o (dot) D r r = o3o3o3x3o |
Volume | 151/1260 = 0.119841 |
Surface | 151 sqrt(7)/180 = 2.219491 |
Dihedral angles
(at margins) | |
Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o3o3o3x3o3o3o . . . . . . . | 70 ♦ 16 | 24 24 | 16 36 16 | 4 24 24 4 | 6 16 6 | 4 4 --------------+----+-----+---------+-------------+---------------+----------+---- . . . x . . . | 2 | 560 | 3 3 | 3 9 3 | 1 9 9 1 | 3 9 3 | 3 3 --------------+----+-----+---------+-------------+---------------+----------+---- . . o3x . . . | 3 | 3 | 560 * | 2 3 0 | 1 6 3 0 | 3 6 1 | 3 2 . . . x3o . . | 3 | 3 | * 560 | 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3 --------------+----+-----+---------+-------------+---------------+----------+---- . o3o3x . . . ♦ 4 | 6 | 4 0 | 280 * * | 1 3 0 0 | 3 3 0 | 3 1 . . o3x3o . . ♦ 6 | 12 | 4 4 | * 420 * | 0 2 2 0 | 1 4 1 | 2 2 . . . x3o3o . ♦ 4 | 6 | 0 4 | * * 280 | 0 0 3 1 | 0 3 3 | 1 3 --------------+----+-----+---------+-------------+---------------+----------+---- o3o3o3x . . . ♦ 5 | 10 | 10 0 | 5 0 0 | 56 * * * | 3 0 0 | 3 0 . o3o3x3o . . ♦ 10 | 30 | 20 10 | 5 5 0 | * 168 * * | 1 2 0 | 2 1 . . o3x3o3o . ♦ 10 | 30 | 10 20 | 0 5 5 | * * 168 * | 0 2 1 | 1 2 . . . x3o3o3o ♦ 5 | 10 | 0 10 | 0 0 5 | * * * 56 | 0 0 3 | 0 3 --------------+----+-----+---------+-------------+---------------+----------+---- o3o3o3x3o . . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 0 | 28 * * | 2 0 . o3o3x3o3o . ♦ 20 | 90 | 60 60 | 15 30 15 | 0 6 6 0 | * 56 * | 1 1 . . o3x3o3o3o ♦ 15 | 60 | 20 60 | 0 15 30 | 0 0 6 6 | * * 28 | 0 2 --------------+----+-----+---------+-------------+---------------+----------+---- o3o3o3x3o3o . ♦ 35 | 210 | 210 140 | 105 105 35 | 21 42 21 0 | 7 7 0 | 8 * . o3o3x3o3o3o ♦ 35 | 210 | 140 210 | 35 105 105 | 0 21 42 21 | 0 7 7 | * 8
or . . . . . . . | 70 ♦ 16 | 48 | 32 36 | 8 48 | 12 16 | 8 -----------------+----+-----+------+---------+---------+-------+--- . . . x . . . | 2 | 560 | 6 | 6 9 | 2 18 | 6 9 | 6 -----------------+----+-----+------+---------+---------+-------+--- . . o3x . . . & | 3 | 3 | 1120 | 2 3 | 1 9 | 4 6 | 5 -----------------+----+-----+------+---------+---------+-------+--- . o3o3x . . . & ♦ 4 | 6 | 4 | 560 * | 1 3 | 3 3 | 4 . . o3x3o . . ♦ 6 | 12 | 8 | * 420 | 0 4 | 2 4 | 4 -----------------+----+-----+------+---------+---------+-------+--- o3o3o3x . . . & ♦ 5 | 10 | 10 | 5 0 | 112 * | 3 0 | 3 . o3o3x3o . . & ♦ 10 | 30 | 30 | 5 5 | * 336 | 1 2 | 3 -----------------+----+-----+------+---------+---------+-------+--- o3o3o3x3o . . & ♦ 15 | 60 | 80 | 30 15 | 6 6 | 56 * | 2 . o3o3x3o3o . ♦ 20 | 90 | 120 | 30 30 | 0 12 | * 56 | 2 -----------------+----+-----+------+---------+---------+-------+--- o3o3o3x3o3o . & ♦ 35 | 210 | 350 | 140 105 | 21 63 | 7 7 | 16
oo3oo3xo3ox3oo3oo&#x → height = 2/sqrt(7) = 0.755929
(bril || inv bril)
o.3o.3o.3o.3o.3o. | 35 * ♦ 12 4 0 | 12 18 12 6 0 0 | 4 18 12 12 18 4 0 0 0 | 6 12 3 4 18 12 1 0 0 0 | 4 3 6 12 3 0 0 | 1 4 3 0
.o3.o3.o3.o3.o3.o | * 35 ♦ 0 4 12 | 0 0 6 12 18 12 | 0 0 0 4 18 12 12 18 4 | 0 0 0 1 12 18 4 3 12 6 | 0 0 3 12 6 3 4 | 0 3 4 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
.. .. x. .. .. .. | 2 0 | 210 * * | 2 3 1 0 0 0 | 1 6 3 2 3 0 0 0 0 | 3 6 1 1 6 3 0 0 0 0 | 3 2 3 6 1 0 0 | 1 3 2 0
oo3oo3oo3oo3oo3oo&#x | 1 1 | * 140 * | 0 0 3 3 0 0 | 0 0 0 3 9 3 0 0 0 | 0 0 0 1 9 9 1 0 0 0 | 0 0 3 9 3 0 0 | 0 3 3 0
.. .. .. .x .. .. | 0 2 | * * 210 | 0 0 0 1 3 2 | 0 0 0 0 3 2 3 6 1 | 0 0 0 0 3 6 1 1 6 3 | 0 0 1 6 3 2 3 | 0 2 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
.. o.3x. .. .. .. | 3 0 | 3 0 0 | 140 * * * * * | 1 3 0 1 0 0 0 0 0 | 3 3 0 1 3 0 0 0 0 0 | 3 1 3 3 0 0 0 | 1 3 1 0
.. .. x.3o. .. .. | 3 0 | 3 0 0 | * 210 * * * * | 0 2 2 0 1 0 0 0 0 | 1 4 1 0 2 2 0 0 0 0 | 2 2 1 4 1 0 0 | 1 2 2 0
.. .. xo .. .. ..&#x | 2 1 | 1 2 0 | * * 210 * * * | 0 0 0 2 3 0 0 0 0 | 0 0 0 1 6 3 0 0 0 0 | 0 0 3 6 1 0 0 | 0 3 2 0
.. .. .. ox .. ..&#x | 1 2 | 0 2 1 | * * * 210 * * | 0 0 0 0 3 2 0 0 0 | 0 0 0 0 3 6 1 0 0 0 | 0 0 1 6 3 0 0 | 0 2 3 0
.. .. .o3.x .. .. | 0 3 | 0 0 3 | * * * * 210 * | 0 0 0 0 1 0 2 2 0 | 0 0 0 0 2 2 0 1 4 1 | 0 0 1 4 1 2 2 | 0 2 2 1
.. .. .. .x3.o .. | 0 3 | 0 0 3 | * * * * * 140 | 0 0 0 0 0 1 0 3 1 | 0 0 0 0 0 3 1 0 3 3 | 0 0 0 3 3 1 3 | 0 1 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 0 0 | 35 * * * * * * * * | 3 0 0 1 0 0 0 0 0 0 | 3 0 3 0 0 0 0 | 1 3 0 0
.. o.3x.3o. .. .. ♦ 6 0 | 12 0 0 | 4 4 0 0 0 0 | * 105 * * * * * * * | 1 2 0 0 1 0 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0
.. .. x.3o.3o. .. ♦ 4 0 | 6 0 0 | 0 4 0 0 0 0 | * * 105 * * * * * * | 0 2 1 0 1 0 0 0 0 0 | 1 2 0 2 1 0 0 | 1 1 2 0
.. oo3xo .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 0 3 0 0 0 | * * * 140 * * * * * | 0 0 0 1 3 0 0 0 0 0 | 0 0 3 3 0 0 0 | 0 3 1 0
.. .. xo3ox .. ..&#x ♦ 3 3 | 3 6 3 | 0 1 3 3 1 0 | * * * * 210 * * * * | 0 0 0 0 2 2 0 0 0 0 | 0 0 1 4 1 0 0 | 0 2 2 0
.. .. .. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0 0 0 3 0 1 | * * * * * 140 * * * | 0 0 0 0 0 3 1 0 0 0 | 0 0 0 3 3 0 0 | 0 1 3 0
.. .o3.o3.x .. .. ♦ 0 4 | 0 0 6 | 0 0 0 0 4 0 | * * * * * * 105 * * | 0 0 0 0 1 0 0 1 2 0 | 0 0 1 2 0 2 1 | 0 2 1 1
.. .. .o3.x3.o .. ♦ 0 6 | 0 0 12 | 0 0 0 0 4 4 | * * * * * * * 105 * | 0 0 0 0 0 1 0 0 2 1 | 0 0 0 2 1 1 2 | 0 1 2 1
.. .. .. .x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 0 0 0 4 | * * * * * * * * 35 | 0 0 0 0 0 0 1 0 0 3 | 0 0 0 0 3 0 3 | 0 0 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o. .. .. ♦ 10 0 | 30 0 0 | 20 10 0 0 0 0 | 5 5 0 0 0 0 0 0 0 | 21 * * * * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0
.. o.3x.3o.3o. .. ♦ 10 0 | 30 0 0 | 10 20 0 0 0 0 | 0 5 5 0 0 0 0 0 0 | * 42 * * * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
.. .. x.3o.3o.3o. ♦ 5 0 | 10 0 0 | 0 10 0 0 0 0 | 0 0 5 0 0 0 0 0 0 | * * 21 * * * * * * * | 0 2 0 0 1 0 0 | 1 0 2 0
oo3oo3xo .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 0 6 0 0 0 | 1 0 0 4 0 0 0 0 0 | * * * 35 * * * * * * | 0 0 3 0 0 0 0 | 0 3 0 0
.. oo3xo3ox .. ..&#x ♦ 6 4 | 12 12 6 | 4 4 12 6 4 0 | 0 1 0 4 4 0 1 0 0 | * * * * 105 * * * * * | 0 0 1 2 0 0 0 | 0 2 1 0
.. .. xo3ox3oo ..&#x ♦ 4 6 | 6 12 12 | 0 4 6 12 4 4 | 0 0 1 0 4 4 0 1 0 | * * * * * 105 * * * * | 0 0 0 2 1 0 0 | 0 1 2 0
.. .. .. ox3oo3oo&#x ♦ 1 4 | 0 4 6 | 0 0 0 6 0 4 | 0 0 0 0 0 4 0 0 1 | * * * * * * 35 * * * | 0 0 0 0 3 0 0 | 0 0 3 0
.o3.o3.o3.x .. .. ♦ 0 5 | 0 0 10 | 0 0 0 0 10 0 | 0 0 0 0 0 0 5 0 0 | * * * * * * * 21 * * | 0 0 1 0 0 2 0 | 0 2 0 1
.. .o3.o3.x3.o .. ♦ 0 10 | 0 0 30 | 0 0 0 0 20 10 | 0 0 0 0 0 0 5 5 0 | * * * * * * * * 42 * | 0 0 0 1 0 1 1 | 0 1 1 1
.. .. .o3.x3.o3.o ♦ 0 10 | 0 0 30 | 0 0 0 0 10 20 | 0 0 0 0 0 0 0 5 5 | * * * * * * * * * 21 | 0 0 0 0 1 0 2 | 0 0 2 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o.3o. .. ♦ 20 0 | 90 0 0 | 60 60 0 0 0 0 | 15 30 15 0 0 0 0 0 0 | 6 6 0 0 0 0 0 0 0 0 | 7 * * * * * * | 1 1 0 0
.. o.3x.3o.3o.3o. ♦ 15 0 | 60 0 0 | 20 60 0 0 0 0 | 0 15 30 0 0 0 0 0 0 | 0 6 6 0 0 0 0 0 0 0 | * 7 * * * * * | 1 0 1 0
oo3oo3xo3ox .. ..&#x ♦ 10 5 | 30 20 10 | 20 10 30 10 10 0 | 5 5 0 20 10 0 5 0 0 | 1 0 0 5 5 0 0 1 0 0 | * * 21 * * * * | 0 2 0 0
.. oo3xo3ox3oo ..&#x ♦ 10 10 | 30 30 30 | 10 20 30 30 20 10 | 0 5 5 10 20 10 5 5 0 | 0 1 0 0 5 5 0 0 1 0 | * * * 42 * * * | 0 1 1 0
.. .. xo3ox3oo3oo&#x ♦ 5 10 | 10 20 30 | 0 10 10 30 10 20 | 0 0 5 0 10 20 0 5 5 | 0 0 1 0 0 5 5 0 0 1 | * * * * 21 * * | 0 0 2 0
.o3.o3.o3.x3.o .. ♦ 0 15 | 0 0 60 | 0 0 0 0 60 20 | 0 0 0 0 0 0 30 15 0 | 0 0 0 0 0 0 0 6 6 0 | * * * * * 7 * | 0 1 0 1
.. .o3.o3.x3.o3.o ♦ 0 20 | 0 0 90 | 0 0 0 0 60 60 | 0 0 0 0 0 0 15 30 15 | 0 0 0 0 0 0 0 0 6 6 | * * * * * * 7 | 0 0 1 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o.3o.3o. ♦ 35 0 | 210 0 0 | 140 210 0 0 0 0 | 35 105 105 0 0 0 0 0 0 | 21 42 21 0 0 0 0 0 0 0 | 7 7 0 0 0 0 0 | 1 * * *
oo3oo3xo3ox3oo ..&#x ♦ 20 15 | 90 60 60 | 60 60 90 60 60 20 | 15 30 15 60 60 20 30 15 0 | 6 6 0 15 30 15 0 6 6 0 | 1 0 6 6 0 1 0 | * 7 * *
.. oo3xo3ox3oo3oo&#x ♦ 15 20 | 60 60 90 | 20 60 60 90 60 60 | 0 15 30 20 60 60 15 30 15 | 0 6 6 0 15 30 15 0 6 6 | 0 1 0 6 6 0 1 | * * 7 *
.o3.o3.o3.x3.o3.o ♦ 0 35 | 0 0 210 | 0 0 0 0 210 140 | 0 0 0 0 0 0 105 105 35 | 0 0 0 0 0 0 0 21 42 21 | 0 0 0 0 0 7 7 | * * * 1
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