|
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 -- o3o3x3o3o3o (bril)
D r -- o3o3o3x3o3o (inv. bril)
where:
R = o3x3o3o3o (rix)
D = o3o3x3o3o (dot)
r = o3o3o3x3o (inv. rix)
|
Lace hyper city
in approx. ASCII-art
|
(bril || inv. bril)
where:
p = x3o3o3o (pen)
r = o3x3o3o (rap)
R = o3o3x3o (alt. rap)
P = o3o3o3x (dual pen)
|
|
Volume
|
151/1260 = 0.119841
|
|
Surface
|
151 sqrt(7)/180 = 2.219491
|
Dihedral angles
(at margins)
|
- at dot between bril and bril: arccos(-1/7) = 98.213211°
- at rix between bril and bril: arccos(1/7) = 81.786789°
|
|
Face vector
|
70, 560, 1120, 980, 448, 112, 16
|
|
Confer
|
- uniform relative:
-
laq
- related segmentoexa:
-
tetdippy
trarapdafup
tetdippa octdip
- general polytopal classes:
-
Wythoffian polyexa
noble polytopes
segmentoexa
fundamental lace prisms
Coxeter-Elte-Gosset polytopes
- analogs:
-
mid-rectified simplex mrSn
|
External
links
|
|
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
oxoo3ooxo xooo3oxoo3ooxo3ooox&#xt → all heights = 2/sqrt(15) = 0.516398
(pen || trarap || bi-inv trarap || dual pen)
o...3o... o...3o...3o...3o... & | 10 * ♦ 4 12 0 0 0 | 6 12 12 18 0 0 0 3 0 | 4 4 12 18 12 18 0 0 0 0 0 0 | 1 4 12 3 6 18 12 0 0 0 | 3 6 12 3 4 0 | 3 5
.o..3.o.. .o..3.o..3.o..3.o.. & | * 60 ♦ 0 2 2 6 6 | 0 4 1 6 1 3 6 9 18 | 0 2 2 3 6 15 3 2 3 12 8 12 | 0 1 3 2 9 7 18 1 5 10 | 1 4 8 7 6 2 | 3 5
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... x... .... .... .... & | 2 0 | 20 * * * * | 3 0 3 0 0 0 0 3 0 | 3 0 3 9 0 0 0 0 0 0 0 0 | 1 1 9 0 0 9 0 0 0 0 | 3 3 9 0 0 0 | 3 3
oo..3oo.. oo..3oo..3oo..3oo..&#x & | 1 1 | * 120 * * * | 0 2 1 3 0 0 0 3 0 | 0 1 2 3 3 6 0 0 0 0 0 0 | 0 1 3 1 3 6 6 0 0 0 | 1 3 6 2 3 0 | 2 4
.x.. .... .... .... .... .... & | 0 2 | * * 60 * * | 0 2 0 0 1 0 0 3 0 | 0 2 1 0 0 6 0 0 3 3 0 0 | 0 1 0 0 9 3 6 0 1 0 | 0 4 3 2 6 0 | 1 5
.... .... .... .x.. .... .... & | 0 2 | * * * 180 * | 0 0 0 1 0 1 2 0 2 | 0 0 0 1 2 2 2 1 0 1 2 4 | 0 0 2 1 1 2 6 1 1 6 | 1 1 5 4 2 2 | 3 3
.oo.3.oo. .oo.3.oo.3.oo.3.oo.&#x | 0 2 | * * * * 180 | 0 0 0 0 0 0 0 2 4 | 0 0 0 0 0 4 0 0 1 4 2 4 | 0 0 0 0 4 2 8 0 2 4 | 0 2 4 4 4 1 | 2 4
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... x...3o... .... .... & | 3 0 | 3 0 0 0 0 | 20 * * * * * * * * | 2 0 0 3 0 0 0 0 0 0 0 0 | 1 0 6 0 0 3 0 0 0 0 | 3 1 6 0 0 0 | 3 2
ox.. .... .... .... .... ....&#x & | 1 2 | 0 2 1 0 0 | * 120 * * * * * * * | 0 1 1 0 0 3 0 0 0 0 0 0 | 0 1 0 0 3 3 3 0 0 0 | 0 3 3 1 3 0 | 1 4
.... .... xo.. .... .... ....&#x & | 2 1 | 1 2 0 0 0 | * * 60 * * * * * * | 0 0 2 3 0 0 0 0 0 0 0 0 | 0 1 3 0 0 6 0 0 0 0 | 1 3 6 0 0 0 | 2 3
.... .... .... ox.. .... ....&#x & | 1 2 | 0 2 0 1 0 | * * * 180 * * * * * | 0 0 0 1 2 2 0 0 0 0 0 0 | 0 0 2 1 1 2 4 0 0 0 | 1 1 4 1 2 0 | 2 3
.x..3.o.. .... .... .... .... & | 0 3 | 0 0 3 0 0 | * * * * 20 * * * * | 0 2 0 0 0 0 0 0 3 0 0 0 | 0 1 0 0 9 0 0 0 0 0 | 0 4 0 0 6 0 | 0 5
.... .... .o..3.x.. .... .... & | 0 3 | 0 0 0 3 0 | * * * * * 60 * * * | 0 0 0 1 0 0 2 0 0 0 2 0 | 0 0 2 0 0 2 0 1 1 4 | 1 1 4 2 0 2 | 3 2
.... .... .... .x..3.o.. .... & | 0 3 | 0 0 0 3 0 | * * * * * * 120 * * | 0 0 0 0 1 0 1 1 0 0 0 2 | 0 0 1 1 0 0 3 1 0 4 | 1 0 3 3 1 2 | 3 2
.xo. .... .... .... .... ....&#x & | 0 3 | 0 0 1 0 2 | * * * * * * * 180 * | 0 0 0 0 0 2 0 0 1 2 0 0 | 0 0 0 0 4 1 4 0 1 0 | 0 2 2 2 4 0 | 1 4
.... .... .... .xo. .... ....&#x & | 0 3 | 0 0 0 1 2 | * * * * * * * * 360 | 0 0 0 0 0 1 0 0 0 1 1 2 | 0 0 0 0 1 1 4 0 1 3 | 0 1 3 3 2 1 | 2 3
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... x...3o...3o... .... & ♦ 4 0 | 6 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 10 * * * * * * * * * * * | 1 0 3 0 0 0 0 0 0 0 | 3 0 3 0 0 0 | 3 1
ox..3oo.. .... .... .... ....&#x & ♦ 1 3 | 0 3 3 0 0 | 0 3 0 0 1 0 0 0 0 | * 40 * * * * * * * * * * | 0 1 0 0 3 0 0 0 0 0 | 0 3 0 0 3 0 | 0 4
ox.. .... xo.. .... .... ....&#x & ♦ 2 2 | 1 4 1 0 0 | 0 2 2 0 0 0 0 0 0 | * * 60 * * * * * * * * * | 0 1 0 0 0 3 0 0 0 0 | 0 3 3 0 0 0 | 1 3
.... .... xo..3ox.. .... ....&#x & ♦ 3 3 | 3 6 0 3 0 | 1 0 3 3 0 1 0 0 0 | * * * 60 * * * * * * * * | 0 0 2 0 0 2 0 0 0 0 | 1 1 4 0 0 0 | 2 2
.... .... .... ox..3oo.. ....&#x & ♦ 1 3 | 0 3 0 3 0 | 0 0 0 3 0 0 1 0 0 | * * * * 120 * * * * * * * | 0 0 1 1 0 0 2 0 0 0 | 1 0 2 2 1 0 | 1 3
oxo. .... .... oxo. .... ....&#xt & ♦ 1 5 | 0 4 2 2 4 | 0 2 0 2 0 0 0 2 2 | * * * * * 180 * * * * * * | 0 0 0 0 1 1 2 0 0 0 | 0 1 2 1 2 0 | 1 3
.... .... .o..3.x..3.o.. .... & ♦ 0 6 | 0 0 0 12 0 | 0 0 0 0 0 4 4 0 0 | * * * * * * 30 * * * * * | 0 0 1 0 0 0 0 1 0 2 | 1 0 2 1 0 2 | 3 1
.... .... .... .x..3.o..3.o.. & ♦ 0 4 | 0 0 0 6 0 | 0 0 0 0 0 0 4 0 0 | * * * * * * * 30 * * * * | 0 0 0 1 0 0 0 1 0 2 | 1 0 1 2 0 2 | 3 1
.xo.3.ox. .... .... .... ....&#x ♦ 0 6 | 0 0 6 0 6 | 0 0 0 0 2 0 0 6 0 | * * * * * * * * 30 * * * | 0 0 0 0 4 0 0 0 0 0 | 0 2 0 0 4 0 | 0 4
.xo. .... .... .... .ox. ....&#x & ♦ 0 4 | 0 0 1 1 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * 180 * * | 0 0 0 0 1 0 2 0 1 0 | 0 1 1 2 2 0 | 1 3
.... .... .oo.3.xo. .... ....&#x & ♦ 0 4 | 0 0 0 3 3 | 0 0 0 0 0 1 0 0 3 | * * * * * * * * * * 120 * | 0 0 0 0 0 1 0 0 1 2 | 0 1 2 2 0 1 | 2 2
.... .... .... .xo.3.ox. ....&#x ♦ 0 6 | 0 0 0 6 6 | 0 0 0 0 0 0 2 0 6 | * * * * * * * * * * * 120 | 0 0 0 0 0 0 2 0 0 2 | 0 0 2 2 1 1 | 2 2
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... x...3o...3o...3o... & ♦ 5 0 | 10 0 0 0 0 | 10 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * | 3 0 0 0 0 0 | 3 0
ox..3oo.. xo.. .... .... ....&#x & ♦ 2 3 | 1 6 3 0 0 | 0 6 3 0 1 0 0 0 0 | 0 2 3 0 0 0 0 0 0 0 0 0 | * 20 * * * * * * * * | 0 3 0 0 0 0 | 0 3
.... .... xo..3ox..3oo.. ....&#x & ♦ 4 6 | 6 12 0 12 0 | 4 0 6 12 0 4 4 0 0 | 1 0 0 4 4 0 1 0 0 0 0 0 | * * 30 * * * * * * * | 1 0 2 0 0 0 | 2 1
.... .... .... ox..3oo..3oo..&#x & ♦ 1 4 | 0 4 0 6 0 | 0 0 0 6 0 0 4 0 0 | 0 0 0 0 4 0 0 1 0 0 0 0 | * * * 30 * * * * * * | 1 0 0 2 0 0 | 2 1
oxo.3oox. .... oxo. .... ....&#xt & ♦ 1 9 | 0 6 9 3 12 | 0 6 0 3 3 0 0 12 6 | 0 2 0 0 0 3 0 0 2 3 0 0 | * * * * 60 * * * * * | 0 1 0 0 2 0 | 0 3
oxo. .... xoo.3oxo. .... ....&#xt & ♦ 3 7 | 3 12 3 6 6 | 1 6 6 6 0 2 0 3 6 | 0 0 3 2 0 3 0 0 0 0 2 0 | * * * * * 60 * * * * | 0 1 2 0 0 0 | 1 2
oxo. .... .... oxo.3oox. ....&#xt & ♦ 1 9 | 0 6 3 9 12 | 0 3 0 6 0 0 3 6 12 | 0 0 0 0 2 3 0 0 0 3 0 2 | * * * * * * 120 * * * | 0 0 1 1 1 0 | 1 2
.... .... .o..3.x..3.o..3.o.. & ♦ 0 10 | 0 0 0 30 0 | 0 0 0 0 0 10 20 0 0 | 0 0 0 0 0 0 5 5 0 0 0 0 | * * * * * * * 6 * * | 1 0 0 0 0 2 | 3 0
.xo. .... .... .... .ox.3.oo.&#x & ♦ 0 5 | 0 0 1 3 6 | 0 0 0 0 0 1 0 3 6 | 0 0 0 0 0 0 0 0 0 3 2 0 | * * * * * * * * 60 * | 0 1 0 2 0 0 | 1 2
.... .... .oo.3.xo.3.ox. ....&#x & ♦ 0 10 | 0 0 0 18 12 | 0 0 0 0 0 4 8 0 18 | 0 0 0 0 0 0 1 1 0 0 4 4 | * * * * * * * * * 60 | 0 0 1 1 0 1 | 2 1
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
.... .... xo..3ox..3oo..3oo..&#x & ♦ 5 10 | 10 20 0 30 0 | 10 0 10 30 0 10 20 0 0 | 5 0 0 10 20 0 5 5 0 0 0 0 | 1 0 5 5 0 0 0 1 0 0 | 6 * * * * * | 2 0
oxo.3oox. xoo.3oxo. .... ....&#xt & ♦ 3 12 | 3 18 12 9 18 | 1 18 9 9 4 3 0 18 18 | 0 6 9 3 0 9 0 0 3 9 6 0 | 0 3 0 0 3 3 0 0 3 0 | * 20 * * * * | 0 2
oxo. .... xoo.3oxo.3oox. ....&#xt & ♦ 4 16 | 6 24 6 30 24 | 4 12 12 24 0 8 12 12 36 | 1 0 6 8 8 12 2 1 0 6 8 8 | 0 0 2 0 0 4 4 0 0 2 | * * 30 * * * | 1 1
oxo. .... .... oxo.3oox.3ooo.&#xt & ♦ 1 14 | 0 8 4 24 24 | 0 4 0 12 0 4 12 12 36 | 0 0 0 0 8 6 1 2 0 12 8 8 | 0 0 0 2 0 0 4 0 4 2 | * * * 30 * * | 1 1
oxoo3ooxo .... oxoo3ooxo ....&#xt ♦ 2 18 | 0 18 18 18 36 | 0 18 0 18 6 0 6 36 36 | 0 6 0 0 6 18 0 0 6 18 0 6 | 0 0 0 0 6 0 6 0 0 0 | * * * * 20 * | 0 2
.... .... .oo.3.xo.3.ox.3.oo.&#x ♦ 0 20 | 0 0 0 60 30 | 0 0 0 0 0 20 40 0 60 | 0 0 0 0 0 0 10 10 0 0 20 20 | 0 0 0 0 0 0 0 2 0 10 | * * * * * 6 | 2 0
------------------------------------+-------+-------------------+---------------------------------+------------------------------------------+------------------------------+-----------------+-----
oxo. .... xoo.3oxo.3oox.3ooo.&#xt & ♦ 5 30 | 10 40 10 90 60 | 10 20 20 60 0 30 60 30 120 | 5 0 10 20 40 30 15 15 0 30 40 40 | 1 0 10 10 0 10 20 3 10 20 | 2 0 5 5 0 2 | 6 *
oxoo3ooxo xooo3oxoo3ooxo ....&#xt & ♦ 5 30 | 6 48 30 54 72 | 4 48 18 54 10 12 24 72 108 | 1 16 18 12 24 54 3 3 12 54 24 24 | 0 6 3 3 18 12 24 0 12 6 | 0 4 3 3 4 0 | * 10
oxooo3ooxoo3oooxo oxooo3ooxoo3oooxo&#xt → all heights = 1/2
(pt || tetdip || octdip || bidual tetdip || pt)
o....3o....3o.... o....3o....3o.... & | 2 * * ♦ 16 0 0 0 | 48 0 0 0 0 | 32 36 0 0 0 0 0 0 | 8 48 0 0 0 | 12 16 0 0 | 8
.o...3.o...3.o... .o...3.o...3.o... & | * 32 * ♦ 1 6 9 0 | 6 6 18 18 0 | 6 9 8 18 18 6 9 0 | 2 18 6 6 24 | 6 10 6 6 | 8
..o..3..o..3..o.. ..o..3..o..3..o.. | * * 36 ♦ 0 0 8 8 | 0 0 8 32 8 | 0 2 0 16 16 16 16 2 | 0 8 8 8 32 | 4 8 8 8 | 8
------------------------------------------+---------+---------------+------------------+-----------------------------+-----------------+-------------+---
oo...3oo...3oo... oo...3oo...3oo...&#x & | 1 1 0 | 32 * * * | 6 0 0 0 0 | 6 9 0 0 0 0 0 0 | 2 18 0 0 0 | 6 9 0 0 | 6
.x... ..... ..... ..... ..... ..... & | 0 2 0 | * 96 * * | 1 2 3 0 0 | 2 3 1 6 3 0 0 0 | 1 9 3 1 6 | 4 6 3 2 | 6
.oo..3.oo..3.oo.. .oo..3.oo..3.oo..&#x & | 0 1 1 | * * 288 * | 0 0 2 4 0 | 0 1 0 4 4 2 4 0 | 0 4 2 2 12 | 2 5 4 4 | 6
..... ..x.. ..... ..... ..... ..... & | 0 0 2 | * * * 144 | 0 0 0 4 2 | 0 0 0 4 2 4 4 1 | 0 2 4 2 12 | 2 4 5 4 | 6
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.x...3.o... ..... ..... ..... ..... & | 0 3 0 | 0 3 0 0 | * 64 * * * | 1 0 1 3 0 0 0 0 | 1 3 3 0 3 | 3 3 3 1 | 5
.xo.. ..... ..... ..... ..... .....&#x & | 0 2 1 | 0 1 2 0 | * * 288 * * | 0 1 0 2 2 0 0 0 | 0 4 1 1 4 | 2 4 2 2 | 5
..... .ox.. ..... ..... ..... .....&#x & | 0 1 2 | 0 0 2 1 | * * * 576 * | 0 0 0 1 1 1 2 0 | 0 1 1 1 7 | 1 3 3 3 | 5
..o..3..x.. ..... ..... ..... ..... & | 0 0 3 | 0 0 0 3 | * * * * 96 | 0 0 0 2 0 2 0 1 | 0 1 4 1 4 | 2 2 4 2 | 5
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oxo.. ..... ..... oxo.. ..... .....&#xt & ♦ 1 4 1 | 4 4 4 0 | 4 0 4 0 0 | * 72 * * * * * * | 0 4 0 0 0 | 2 4 0 0 | 4
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..... .ox..3.oo.. ..... ..... .....&#x & ♦ 0 1 3 | 0 0 3 3 | 0 0 0 3 1 | * * * * * 192 * * | 0 0 1 1 2 | 1 1 2 2 | 4
..... .oxo. ..... ..... .oxo. .....&#x ♦ 0 2 4 | 0 0 8 4 | 0 0 0 8 0 | * * * * * * 144 * | 0 0 0 0 4 | 0 2 2 2 | 4
..o..3..x..3..o.. ..... ..... ..... & ♦ 0 0 6 | 0 0 0 12 | 0 0 0 0 8 | * * * * * * * 12 | 0 0 4 0 0 | 2 0 4 0 | 4
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oxo..3oox.. ..... oxo.. ..... .....&#xt & ♦ 1 6 3 | 6 9 12 3 | 9 2 12 6 1 | 2 3 0 2 3 0 0 0 | * 96 * * * | 1 2 0 0 | 3
.xo..3.ox..3.oo.. ..... ..... .....&#x & ♦ 0 4 6 | 0 6 12 12 | 0 4 6 12 8 | 0 0 1 4 0 4 0 1 | * * 48 * * | 1 0 2 0 | 3
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oxoo.3ooxo. ..... oxoo.3ooxo. .....&#xt & ♦ 1 10 9 | 9 18 45 18 | 18 6 36 54 6 | 6 9 0 12 18 6 9 0 | 0 6 0 0 6 | * 32 * * | 2
.xoo.3.oxo.3.oox. ..... .oxo. .....&#xt & ♦ 0 8 12 | 0 12 48 30 | 0 8 24 72 16 | 0 0 2 16 12 16 12 2 | 0 0 4 0 8 | * * 24 * | 2
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