|
Acronym
|
roc
|
|
Name
|
rectified octaexon,
vertex figure of hocto,
Gosset polytope 05,1
|
|
Circumradius
|
sqrt(3)/2 = 0.866025
|
Inradius
wrt. hop
|
3/sqrt(28) = 0.566947
|
Inradius
wrt. ril
|
1/sqrt(28) = 0.188982
|
Lace city
in approx. ASCII-art
|
_+---------------------- o o3o3o3o3o (pt)
_/ _+------------ x x3o3o3o3o (hixip)
_/ _/ _+-- o o3x3o3o3o (rix)
/ / /
o3o3o3o3o x3o3o3o3o -- x3o3o3o3o3o (hop)
x3o3o3o3o o3x3o3o3o -- o3x3o3o3o3o (ril)
|
_+------------------------ x3o o3o3o3o ({3})
_/ _+------------- o3x x3o3o3o ({3}-dual trapen)
_/ _/ _+-- o3o o3x3o3o (rap)
/ / /
x o3o3o3o o x3o3o3o -- x3o3o3o3o3o (hop)
o o3o3o3o x x3o3o3o o o3x3o3o -- o3x3o3o3o3o (ril)
\ \ \
\ \ +-- o o3x3o3o3o (rix)
\ +-------------- x x3o3o3o3o (hixip)
+-------------------------- o o3o3o3o3o (pt)
|
Lace hyper city
in approx. ASCII-art
|
 ©
|
o3x3o3o
rap
|
x3o3o3o
x3o3o3o
x3o3o3o
{3}-dual trapen
|
o3o3o3o
o3o3o3o
o3o3o3o
perp {3}
|
or
+------------------------------ o3o o3x3o3o (rap)
/ +---------------- o3x x3o3o3o ({3}-dual trapen)
/ / +-- x3o o3o3o3o ({3})
/ / /
|
x3o3o
x3o3o o3o layer of hop
|
o3o3o
o3o3o
o3o3o
o3o3o o3x layer of hop
|
|
o3x3o
o3x3o o3o layer of ril
|
x3o3o
x3o3o
x3o3o
x3o3o o3x layer of ril
|
o3o3o
o3o3o
o3o3o
o3o3o x3o layer of ril
|
\_ \_ \_
\_ \_ +-- o3x3o o3o3o (oct)
\_ +-------------- x3o3o x3o3o (tetdip)
+-------------------------- o3o3o o3x3o (perp oct)
|
|
|
Coordinates
|
-
(1, 1, 0, 1, 0, 0, 0)/2 & all cyclic permutations, all even changes of sign
|
|
Volume
|
1/168 = 0.0059524
|
|
Surface
|
29 sqrt(7)/360 = 0.213130
|
Dihedral angles
(at margins)
|
- at hix between hop and ril: arccos(-1/7) = 98.213211°
- at rix between ril and ril: arccos(1/7) = 81.786789°
|
|
Face vector
|
28, 168, 336, 350, 224, 84, 16
|
|
Confer
|
- uniform relative:
-
naq
- related segmentoexa:
-
rixahixip
rapatrapen
octatetdip
trial trapen
hixippy
tedroc
- general polytopal classes:
-
Wythoffian polyexa
segmentoexa
fundamental lace prisms
Coxeter-Elte-Gosset polytopes
- analogs:
-
rectified simplex rSn
|
External
links
|
|
Incidence matrix according to Dynkin symbol
o3x3o3o3o3o3o
. . . . . . . | 28 ♦ 12 | 6 30 | 15 40 | 20 30 | 15 12 | 6 2
--------------+----+-----+--------+--------+--------+-------+----
. x . . . . . | 2 | 168 | 1 5 | 5 10 | 10 10 | 10 5 | 5 1
--------------+----+-----+--------+--------+--------+-------+----
o3x . . . . . | 3 | 3 | 56 * ♦ 5 0 | 10 0 | 10 0 | 5 0
. x3o . . . . | 3 | 3 | * 280 | 1 4 | 4 6 | 6 4 | 4 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o . . . . ♦ 6 | 12 | 4 4 | 70 * ♦ 4 0 | 6 0 | 4 0
. x3o3o . . . ♦ 4 | 6 | 0 4 | * 280 | 1 3 | 3 3 | 3 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o . . . ♦ 10 | 30 | 10 20 | 5 5 | 56 * | 3 0 | 3 0
. x3o3o3o . . ♦ 5 | 10 | 0 10 | 0 5 | * 168 | 1 2 | 2 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o3o . . ♦ 15 | 60 | 20 60 | 15 30 | 6 6 | 28 * | 2 0
. x3o3o3o3o . ♦ 6 | 15 | 0 20 | 0 15 | 0 6 | * 56 | 1 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o3o3o . ♦ 21 | 105 | 35 140 | 35 105 | 21 42 | 7 7 | 8 *
. x3o3o3o3o3o ♦ 7 | 21 | 0 35 | 0 35 | 0 21 | 0 7 | * 8
xo3ox3oo3oo3oo3oo&#x → height = 2/sqrt(7) = 0.755929
(hop || ril)
o.3o.3o.3o.3o.3o. | 7 * ♦ 6 6 0 | 15 6 15 0 0 | 20 15 20 0 0 | 15 20 15 0 0 | 6 15 6 0 0 | 1 6 1 0
.o3.o3.o3.o3.o3.o | * 21 ♦ 0 2 10 | 0 1 10 5 20 | 0 5 20 10 20 | 0 10 20 10 10 | 0 10 10 5 2 | 0 5 2 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x. .. .. .. .. .. | 2 0 | 21 * * | 5 1 0 0 0 | 10 5 0 0 0 | 10 10 0 0 0 | 5 10 0 0 0 | 1 5 0 0
oo3oo3oo3oo3oo3oo&#x | 1 1 | * 42 * | 0 1 5 0 0 | 0 5 10 0 0 | 0 10 10 0 0 | 0 10 5 0 0 | 0 5 1 0
.. .x .. .. .. .. | 0 2 | * * 105 | 0 0 1 1 4 | 0 1 4 4 6 | 0 4 6 6 4 | 0 6 4 4 1 | 0 4 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o. .. .. .. .. | 3 0 | 3 0 0 | 35 * * * * | 4 1 0 0 0 | 6 4 0 0 0 | 4 6 0 0 0 | 1 4 0 0
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 21 * * * ♦ 0 5 0 0 0 | 0 10 0 0 0 | 0 10 0 0 0 | 0 5 0 0
.. ox .. .. .. ..&#x | 1 2 | 0 2 1 | * * 105 * * | 0 1 4 0 0 | 0 4 6 0 0 | 0 6 4 0 0 | 0 4 1 0
.o3.x .. .. .. .. | 0 3 | 0 0 3 | * * * 35 * ♦ 0 1 0 4 0 | 0 4 0 6 0 | 0 6 0 4 0 | 0 4 0 1
.. .x3.o .. .. .. | 0 3 | 0 0 3 | * * * * 140 | 0 0 1 1 3 | 0 1 3 3 3 | 0 3 3 3 1 | 0 3 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 0 | 35 * * * * | 3 1 0 0 0 | 3 3 0 0 0 | 1 3 0 0
xo3ox .. .. .. ..&#x ♦ 3 3 | 3 6 3 | 1 3 3 1 0 | * 35 * * * ♦ 0 4 0 0 0 | 0 6 0 0 0 | 0 4 0 0
.. ox3oo .. .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 0 1 | * * 140 * * | 0 1 3 0 0 | 0 3 3 0 0 | 0 3 1 0
.o3.x3.o .. .. .. ♦ 0 6 | 0 0 12 | 0 0 0 4 4 | * * * 35 * ♦ 0 1 0 3 0 | 0 3 0 3 0 | 0 3 0 1
.. .x3.o3.o .. .. ♦ 0 4 | 0 0 6 | 0 0 0 0 4 | * * * * 105 | 0 0 1 1 2 | 0 1 2 2 1 | 0 2 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o.3o. .. .. ♦ 5 0 | 10 0 0 | 10 0 0 0 0 | 5 0 0 0 0 | 21 * * * * | 2 1 0 0 0 | 1 2 0 0
xo3ox3oo .. .. ..&#x ♦ 4 6 | 6 12 12 | 4 6 12 4 4 | 1 4 4 1 0 | * 35 * * * | 0 3 0 0 0 | 0 3 0 0
.. ox3oo3oo .. ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 0 4 | 0 0 4 0 1 | * * 105 * * | 0 1 2 0 0 | 0 2 1 0
.o3.x3.o3.o .. .. ♦ 0 10 | 0 0 30 | 0 0 0 10 20 | 0 0 0 5 5 | * * * 21 * | 0 1 0 2 0 | 0 2 0 1
.. .x3.o3.o3.o .. ♦ 0 5 | 0 0 10 | 0 0 0 0 10 | 0 0 0 0 5 | * * * * 42 | 0 0 1 1 1 | 0 1 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o.3o.3o. .. ♦ 6 0 | 15 0 0 | 20 0 0 0 0 | 15 0 0 0 0 | 6 0 0 0 0 | 7 * * * * | 1 1 0 0
xo3ox3oo3oo .. ..&#x ♦ 5 10 | 10 20 30 | 10 10 30 10 20 | 5 10 20 5 5 | 1 5 5 1 0 | * 21 * * * | 0 2 0 0
.. ox3oo3oo3oo ..&#x ♦ 1 5 | 0 5 10 | 0 0 10 0 10 | 0 0 10 0 5 | 0 0 5 0 1 | * * 42 * * | 0 1 1 0
.o3.x3.o3.o3.o .. ♦ 0 15 | 0 0 60 | 0 0 0 20 60 | 0 0 0 15 30 | 0 0 0 6 6 | * * * 7 * | 0 1 0 1
.. .x3.o3.o3.o3.o ♦ 0 6 | 0 0 15 | 0 0 0 0 20 | 0 0 0 0 15 | 0 0 0 0 6 | * * * * 7 | 0 0 1 1
---------------------+------+-----------+------------------+------------------+-----------------+-------------+--------
x.3o.3o.3o.3o.3o. ♦ 7 0 | 21 0 0 | 35 0 0 0 0 | 35 0 0 0 0 | 21 0 0 0 0 | 7 0 0 0 0 | 1 * * *
xo3ox3oo3oo3oo ..&#x ♦ 6 15 | 15 30 60 | 20 15 60 20 60 | 15 20 60 15 30 | 6 15 30 6 6 | 1 6 6 1 0 | * 7 * *
.. ox3oo3oo3oo3oo&#x ♦ 1 6 | 0 6 15 | 0 0 15 0 20 | 0 0 20 0 15 | 0 0 15 0 6 | 0 0 6 0 1 | * * 7 *
.o3.x3.o3.o3.o3.o ♦ 0 21 | 0 0 105 | 0 0 0 35 140 | 0 0 0 35 105 | 0 0 0 21 42 | 0 0 0 7 7 | * * * 1
oxo oxo3oox3ooo3ooo3ooo&#xt → both heights = 1/sqrt(3) = 0.577350
(pt || hixip || rix)
o.. o..3o..3o..3o..3o.. | 1 * * ♦ 12 0 0 0 0 | 6 30 0 0 0 0 0 0 | 15 40 0 0 0 0 0 0 | 20 30 0 0 0 0 0 0 | 15 12 0 0 0 0 0 | 6 2 0 0
.o. .o.3.o.3.o.3.o.3.o. | * 12 * ♦ 1 1 5 5 0 | 1 5 10 5 5 10 0 0 | 5 10 10 10 10 10 0 0 | 10 10 5 10 10 5 0 0 | 10 5 1 5 5 1 0 | 5 1 1 1
..o ..o3..o3..o3..o3..o | * * 15 ♦ 0 0 0 4 8 | 0 0 0 2 2 16 4 12 | 1 0 0 8 8 24 6 8 | 4 0 0 12 12 16 4 2 | 6 0 0 8 8 4 1 | 4 0 2 2
----------------------------+---------+---------------+-------------------------+--------------------------+-----------------------+--------------------+--------
oo. oo.3oo.3oo.3oo.3oo.&#x | 1 1 0 | 12 * * * * | 1 5 0 0 0 0 0 0 | 5 10 0 0 0 0 0 0 | 10 10 0 0 0 0 0 0 | 10 5 0 0 0 0 0 | 5 1 0 0
.x. ... ... ... ... ... | 0 2 0 | * 6 * * * | 1 0 0 5 0 0 0 0 | 5 0 0 10 0 0 0 0 | 10 0 0 10 0 0 0 0 | 10 0 0 5 0 0 0 | 5 0 1 0
... .x. ... ... ... ... | 0 2 0 | * * 30 * * | 0 1 4 0 1 0 0 0 | 1 4 6 0 4 0 0 0 | 4 6 4 0 6 0 0 0 | 6 4 1 0 4 0 0 | 4 1 0 1
.oo .oo3.oo3.oo3.oo3.oo&#x | 0 1 1 | * * * 60 * | 0 0 0 1 1 4 0 0 | 1 0 0 4 4 6 0 0 | 4 0 0 6 6 4 0 0 | 6 0 0 4 4 1 0 | 4 0 1 1
... ... ..x ... ... ... | 0 0 2 | * * * * 60 | 0 0 0 0 0 2 1 3 | 0 0 0 1 2 6 3 3 | 1 0 0 3 6 6 3 1 | 3 0 0 3 6 2 1 | 3 0 1 2
----------------------------+---------+---------------+-------------------------+--------------------------+-----------------------+--------------------+--------
ox. ... ... ... ... ...&#x | 1 2 0 | 2 1 0 0 0 | 6 * * * * * * * ♦ 5 0 0 0 0 0 0 0 | 10 0 0 0 0 0 0 0 | 10 0 0 0 0 0 0 | 5 0 0 0
... ox. ... ... ... ...&#x | 1 2 0 | 2 0 1 0 0 | * 30 * * * * * * | 1 4 0 0 0 0 0 0 | 4 6 0 0 0 0 0 0 | 6 4 0 0 0 0 0 | 4 1 0 0
... .x.3.o. ... ... ... | 0 3 0 | 0 0 3 0 0 | * * 40 * * * * * | 0 1 3 0 1 0 0 0 | 1 3 3 0 3 0 0 0 | 3 3 1 0 3 0 0 | 3 1 0 1
.xo ... ... ... ... ...&#x | 0 2 1 | 0 1 0 2 0 | * * * 30 * * * * | 1 0 0 4 0 0 0 0 | 4 0 0 6 0 0 0 0 | 6 0 0 4 0 0 0 | 4 0 1 0
... .xo ... ... ... ...&#x | 0 2 1 | 0 0 1 2 0 | * * * * 30 * * * ♦ 1 0 0 0 4 0 0 0 | 4 0 0 0 6 0 0 0 | 6 0 0 0 4 0 0 | 4 0 0 1
... ... .ox ... ... ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 120 * * | 0 0 0 1 1 3 0 0 | 1 0 0 3 3 3 0 0 | 3 0 0 3 3 1 0 | 3 0 1 1
... ..o3..x ... ... ... | 0 0 3 | 0 0 0 0 3 | * * * * * * 20 * ♦ 0 0 0 0 2 0 3 0 | 1 0 0 0 6 0 3 0 | 3 0 0 0 6 0 1 | 3 0 0 2
... ... ..x3..o ... ... | 0 0 3 | 0 0 0 0 3 | * * * * * * * 60 | 0 0 0 0 0 2 1 2 | 0 0 0 1 2 4 2 1 | 1 0 0 2 4 2 1 | 2 0 1 2
----------------------------+---------+---------------+-------------------------+--------------------------+-----------------------+--------------------+--------
oxo oxo ... ... ... ...&#xt ♦ 1 4 1 | 4 2 2 4 0 | 2 2 0 2 2 0 0 0 | 15 * * * * * * * ♦ 4 0 0 0 0 0 0 0 | 6 0 0 0 0 0 0 | 4 0 0 0
... ox.3oo. ... ... ...&#x ♦ 1 3 0 | 3 0 3 0 0 | 0 3 1 0 0 0 0 0 | * 40 * * * * * * | 1 3 0 0 0 0 0 0 | 3 3 0 0 0 0 0 | 3 1 0 0
... .x.3.o.3.o. ... ... ♦ 0 4 0 | 0 0 6 0 0 | 0 0 4 0 0 0 0 0 | * * 30 * * * * * | 0 1 2 0 1 0 0 0 | 1 2 1 0 2 0 0 | 2 1 0 1
.xo ... .ox ... ... ...&#x ♦ 0 2 2 | 0 1 0 4 1 | 0 0 0 2 0 2 0 0 | * * * 60 * * * * | 1 0 0 3 0 0 0 0 | 3 0 0 3 0 0 0 | 3 0 1 0
... .xo3.ox ... ... ...&#x ♦ 0 3 3 | 0 0 3 6 3 | 0 0 1 0 3 3 1 0 | * * * * 40 * * * ♦ 1 0 0 0 3 0 0 0 | 3 0 0 0 3 0 0 | 3 0 0 1
... ... .ox3.oo ... ...&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 0 3 0 1 | * * * * * 120 * * | 0 0 0 1 1 2 0 0 | 1 0 0 2 2 1 0 | 2 0 1 1
... ..o3..x3..o ... ... ♦ 0 0 6 | 0 0 0 0 12 | 0 0 0 0 0 0 4 4 | * * * * * * 15 * ♦ 0 0 0 0 2 0 2 0 | 1 0 0 0 4 0 1 | 2 0 0 2
... ... ..x3..o3..o ... ♦ 0 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 0 4 | * * * * * * * 30 | 0 0 0 0 0 2 1 1 | 0 0 0 1 2 2 1 | 1 0 1 2
----------------------------+---------+---------------+-------------------------+--------------------------+-----------------------+--------------------+--------
oxo oxo3oox ... ... ...&#xt ♦ 1 6 3 | 6 3 6 12 3 | 3 6 2 6 6 6 1 0 | 3 2 0 3 2 0 0 0 | 20 * * * * * * * | 3 0 0 0 0 0 0 | 3 0 0 0
... ox.3oo.3oo. ... ...&#x ♦ 1 4 0 | 4 0 6 0 0 | 0 6 4 0 0 0 0 0 | 0 4 1 0 0 0 0 0 | * 30 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
... .x.3.o.3.o.3.o. ... ♦ 0 5 0 | 0 0 10 0 0 | 0 0 10 0 0 0 0 0 | 0 0 5 0 0 0 0 0 | * * 12 * * * * * | 0 1 1 0 1 0 0 | 1 1 0 1
.xo ... .ox3.oo ... ...&#x ♦ 0 2 3 | 0 1 0 6 3 | 0 0 0 3 0 6 0 1 | 0 0 0 3 0 2 0 0 | * * * 60 * * * * | 1 0 0 2 0 0 0 | 2 0 1 0
... .xo3.ox3.oo ... ...&#x ♦ 0 4 6 | 0 0 6 12 12 | 0 0 4 0 6 12 4 4 | 0 0 1 0 4 4 1 0 | * * * * 30 * * * | 1 0 0 0 2 0 0 | 2 0 0 1
... ... .ox3.oo3.oo ...&#x ♦ 0 1 4 | 0 0 0 4 6 | 0 0 0 0 0 6 0 4 | 0 0 0 0 0 4 0 1 | * * * * * 60 * * | 0 0 0 1 1 1 0 | 1 0 1 1
... ..o3..x3..o3..o ... ♦ 0 0 10 | 0 0 0 0 30 | 0 0 0 0 0 0 10 20 | 0 0 0 0 0 0 5 5 | * * * * * * 6 * | 0 0 0 0 2 0 1 | 1 0 0 2
... ... ..x3..o3..o3..o ♦ 0 0 5 | 0 0 0 0 10 | 0 0 0 0 0 0 0 10 | 0 0 0 0 0 0 0 5 | * * * * * * * 6 | 0 0 0 0 0 2 1 | 0 0 1 2
----------------------------+---------+---------------+-------------------------+--------------------------+-----------------------+--------------------+--------
oxo oxo3oox3ooo ... ...&#xt ♦ 1 8 6 | 8 4 12 24 12 | 4 12 8 12 12 24 4 4 | 6 8 2 12 8 8 1 0 | 4 2 0 4 2 0 0 0 | 15 * * * * * * | 2 0 0 0
... ox.3oo.3oo.3oo. ...&#x ♦ 1 5 0 | 5 0 10 0 0 | 0 10 10 0 0 0 0 0 | 0 10 5 0 0 0 0 0 | 0 5 1 0 0 0 0 0 | * 12 * * * * * | 1 1 0 0
... .x.3.o.3.o.3.o.3.o. ♦ 0 6 0 | 0 0 15 0 0 | 0 0 20 0 0 0 0 0 | 0 0 15 0 0 0 0 0 | 0 0 6 0 0 0 0 0 | * * 2 * * * * | 0 1 0 1
.xo ... .ox3.oo3.oo ...&#x ♦ 0 2 4 | 0 1 0 8 6 | 0 0 0 4 0 12 0 4 | 0 0 0 6 0 8 0 1 | 0 0 0 4 0 2 0 0 | * * * 30 * * * | 1 0 1 0
... .xo3.ox3.oo3.oo ...&#x ♦ 0 5 10 | 0 0 10 20 30 | 0 0 10 0 10 30 10 20 | 0 0 5 0 10 20 5 5 | 0 0 1 0 5 5 1 0 | * * * * 12 * * | 1 0 0 1
... ... .ox3.oo3.oo3.oo&#x ♦ 0 1 5 | 0 0 0 5 10 | 0 0 0 0 0 10 0 10 | 0 0 0 0 0 10 0 5 | 0 0 0 0 0 5 0 1 | * * * * * 12 * | 0 0 1 1
... ..o3..x3..o3..o3..o ♦ 0 0 15 | 0 0 0 0 60 | 0 0 0 0 0 0 20 60 | 0 0 0 0 0 0 15 30 | 0 0 0 0 0 0 6 6 | * * * * * * 1 | 0 0 0 2
----------------------------+---------+---------------+-------------------------+--------------------------+-----------------------+--------------------+--------
oxo oxo3oox3ooo3ooo ...&#xt ♦ 1 10 10 | 10 5 20 40 30 | 5 20 20 20 20 60 10 20 | 10 20 10 30 20 40 5 5 | 10 10 2 20 10 10 1 0 | 5 2 0 5 5 0 0 | 6 * * *
... ox.3oo.3oo.3oo.3oo.&#xt ♦ 1 6 0 | 6 0 15 0 0 | 0 15 20 0 0 0 0 0 | 0 20 15 0 0 0 0 0 | 0 15 6 0 0 0 0 0 | 0 6 1 0 0 0 0 | * 2 * *
.xo ... .ox3.oo3.oo3.oo&#x ♦ 0 2 5 | 0 1 0 10 10 | 0 0 0 5 0 20 0 10 | 0 0 0 10 0 20 0 5 | 0 0 0 10 0 10 0 1 | 0 0 0 5 0 2 0 | * * 6 *
... .xo3.ox3.oo3.oo3.oo&#x ♦ 0 6 15 | 0 0 15 30 60 | 0 0 20 0 15 60 20 60 | 0 0 15 0 20 60 15 30 | 0 0 6 0 15 30 6 6 | 0 0 1 0 6 6 1 | * * * 2
xoo3oxo oxo3oox3ooo3ooo&#xt → both heights = 2/sqrt(15) = 0.516398
({3} || pseudo {3}-dual trapen || rap)
o..3o.. o..3o..3o..3o.. | 3 * * ♦ 2 10 0 0 0 0 | 1 10 5 20 0 0 0 0 0 0 0 | 5 20 10 20 0 0 0 0 0 0 0 | 10 20 10 10 0 0 0 0 0 0 | 10 10 5 2 0 0 0 | 5 2 1 0
.o.3.o. .o.3.o.3.o.3.o. | * 15 * ♦ 0 2 2 4 4 0 | 0 1 2 8 1 6 8 4 6 0 0 | 1 4 8 12 4 4 12 6 4 0 0 | 4 6 12 8 1 6 8 4 1 0 | 6 4 8 2 4 2 1 | 4 1 2 1
..o3..o ..o3..o3..o3..o | * * 10 ♦ 0 0 0 0 6 6 | 0 0 0 0 0 0 6 3 18 3 6 | 0 0 3 0 0 2 18 9 18 3 2 | 1 0 9 0 0 6 18 9 6 1 | 3 0 9 0 6 6 3 | 3 0 3 2
----------------------------+---------+------------------+--------------------------------+-------------------------------+-----------------------------+--------------------+--------
x.. ... ... ... ... ... | 2 0 0 | 3 * * * * * | 1 5 0 0 0 0 0 0 0 0 0 | 5 10 0 0 0 0 0 0 0 0 0 | 10 10 0 0 0 0 0 0 0 0 | 10 5 0 0 0 0 0 | 5 1 0 0
oo.3oo. oo.3oo.3oo.3oo.&#x | 1 1 0 | * 30 * * * * | 0 1 1 4 0 0 0 0 0 0 0 | 1 4 4 6 0 0 0 0 0 0 0 | 4 6 6 4 0 0 0 0 0 0 | 6 4 4 1 0 0 0 | 4 1 1 0
... .x. ... ... ... ... | 0 2 0 | * * 15 * * * | 0 0 1 0 1 0 4 0 0 0 0 | 1 0 4 0 0 4 6 0 0 0 0 | 4 0 6 0 0 6 4 0 0 0 | 6 0 4 0 4 1 0 | 4 0 1 1
... ... .x. ... ... ... | 0 2 0 | * * * 30 * * | 0 0 0 2 0 3 0 1 0 0 0 | 0 1 2 6 3 0 0 3 0 0 0 | 1 3 6 6 1 0 0 3 0 0 | 3 3 6 2 0 0 1 | 3 1 2 0
.oo3.oo .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * * 60 * | 0 0 0 0 0 0 2 1 3 0 0 | 0 0 2 0 0 1 6 3 3 0 0 | 1 0 6 0 0 3 6 3 1 0 | 3 0 6 0 3 2 1 | 3 0 2 1
... ... ... ..x ... ... | 0 0 2 | * * * * * 30 | 0 0 0 0 0 0 0 0 3 1 2 | 0 0 0 0 0 0 3 3 6 2 1 | 0 0 3 0 0 1 6 6 3 1 | 1 0 6 0 2 3 3 | 2 0 3 1
----------------------------+---------+------------------+--------------------------------+-------------------------------+-----------------------------+--------------------+--------
x..3o.. ... ... ... ... | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * * * ♦ 5 0 0 0 0 0 0 0 0 0 0 | 10 0 0 0 0 0 0 0 0 0 | 10 0 0 0 0 0 0 | 5 0 0 0
xo. ... ... ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 15 * * * * * * * * * | 1 4 0 0 0 0 0 0 0 0 0 | 4 6 0 0 0 0 0 0 0 0 | 6 4 0 0 0 0 0 | 4 1 0 0
... ox. ... ... ... ...&#x | 1 2 0 | 0 2 1 0 0 0 | * * 15 * * * * * * * * ♦ 1 0 4 0 0 0 0 0 0 0 0 | 4 0 6 0 0 0 0 0 0 0 | 6 0 4 0 0 0 0 | 4 0 1 0
... ... ox. ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * * 60 * * * * * * * | 0 1 1 3 0 0 0 0 0 0 0 | 1 3 3 3 0 0 0 0 0 0 | 3 3 3 1 0 0 0 | 3 1 1 0
.o.3.x. ... ... ... ... | 0 3 0 | 0 0 3 0 0 0 | * * * * 5 * * * * * * | 1 0 0 0 0 4 0 0 0 0 0 | 4 0 0 0 0 6 0 0 0 0 | 6 0 0 0 4 0 0 | 4 0 0 1
... ... .x.3.o. ... ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * 30 * * * * * | 0 0 0 2 2 0 0 1 0 0 0 | 0 1 2 4 1 0 0 2 0 0 | 1 2 4 2 0 0 1 | 2 1 2 0
... .xo ... ... ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * * * 60 * * * * | 0 0 1 0 0 1 3 0 0 0 0 | 1 0 3 0 0 3 3 0 0 0 | 3 0 3 0 3 1 0 | 3 0 1 1
... ... .xo ... ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * * 30 * * * ♦ 0 0 2 0 0 0 0 3 0 0 0 | 1 0 6 0 0 0 0 3 0 0 | 3 0 6 0 0 0 1 | 3 0 2 0
... ... ... .ox ... ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * * 90 * * | 0 0 0 0 0 0 2 1 2 0 0 | 0 0 2 0 0 1 4 2 1 0 | 1 0 4 0 2 2 1 | 2 0 2 1
... ... ..o3..x ... ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * 10 * ♦ 0 0 0 0 0 0 0 3 0 2 0 | 0 0 3 0 0 0 0 6 0 1 | 1 0 6 0 0 0 3 | 2 0 3 0
... ... ... ..x3..o ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * 20 | 0 0 0 0 0 0 0 0 3 1 1 | 0 0 0 0 0 0 3 3 3 1 | 0 0 3 0 1 3 3 | 1 0 3 1
----------------------------+---------+------------------+--------------------------------+-------------------------------+-----------------------------+--------------------+--------
xo.3ox. ... ... ... ...&#x ♦ 3 3 0 | 3 6 3 0 0 0 | 1 3 3 0 1 0 0 0 0 0 0 | 5 * * * * * * * * * * ♦ 4 0 0 0 0 0 0 0 0 0 | 6 0 0 0 0 0 0 | 4 0 0 0
xo. ... ox. ... ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 0 2 0 0 0 0 0 0 0 | * 30 * * * * * * * * * | 1 3 0 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 | 3 1 0 0
... oxo oxo ... ... ...&#xt ♦ 1 4 1 | 0 4 2 2 4 0 | 0 0 2 2 0 0 2 2 0 0 0 | * * 30 * * * * * * * * ♦ 1 0 3 0 0 0 0 0 0 0 | 3 0 3 0 0 0 0 | 3 0 1 0
... ... ox.3oo. ... ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 0 3 0 1 0 0 0 0 0 | * * * 60 * * * * * * * | 0 1 1 2 0 0 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
... ... .x.3.o.3.o. ... ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 4 0 0 0 0 0 | * * * * 15 * * * * * * | 0 0 0 2 1 0 0 1 0 0 | 0 1 2 2 0 0 1 | 1 1 2 0
.oo3.xo ... ... ... ...&#x ♦ 0 3 1 | 0 0 3 0 3 0 | 0 0 0 0 1 0 3 0 0 0 0 | * * * * * 20 * * * * * | 1 0 0 0 0 3 0 0 0 0 | 3 0 0 0 3 0 0 | 3 0 0 1
... .xo ... .ox ... ...&#x ♦ 0 2 2 | 0 0 1 0 4 1 | 0 0 0 0 0 0 2 0 2 0 0 | * * * * * * 90 * * * * | 0 0 1 0 0 1 2 0 0 0 | 1 0 2 0 2 1 0 | 2 0 1 1
... ... .xo3.ox ... ...&#x ♦ 0 3 3 | 0 0 0 3 6 3 | 0 0 0 0 0 1 0 3 3 1 0 | * * * * * * * 30 * * * ♦ 0 0 2 0 0 0 0 2 0 0 | 1 0 4 0 0 0 1 | 2 0 2 0
... ... ... .ox3.oo ...&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 3 0 1 | * * * * * * * * 60 * * | 0 0 0 0 0 0 2 1 1 0 | 0 0 2 0 1 2 1 | 1 0 2 1
... ... ..o3..x3..o ... ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * 5 * ♦ 0 0 0 0 0 0 0 3 0 1 | 0 0 3 0 0 0 3 | 1 0 3 0
... ... ... ..x3..o3..o ♦ 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * 5 | 0 0 0 0 0 0 0 0 3 1 | 0 0 0 0 0 3 3 | 0 0 3 1
----------------------------+---------+------------------+--------------------------------+-------------------------------+-----------------------------+--------------------+--------
xoo3oxo oxo ... ... ...&#xt ♦ 3 6 1 | 3 12 6 3 6 0 | 1 6 6 6 2 0 6 3 0 0 0 | 2 3 3 0 0 2 0 0 0 0 0 | 10 * * * * * * * * * | 3 0 0 0 0 0 0 | 3 0 0 0
xo. ... ox.3oo. ... ...&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 0 3 0 6 0 1 0 0 0 0 0 | 0 3 0 2 0 0 0 0 0 0 0 | * 30 * * * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
... oxo oxo3oox ... ...&#xt ♦ 1 6 3 | 0 6 3 6 12 3 | 0 0 3 6 0 2 6 6 6 1 0 | 0 0 3 2 0 0 3 2 0 0 0 | * * 30 * * * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0
... ... ox.3oo.3oo. ...&#x ♦ 1 4 0 | 0 4 0 6 0 0 | 0 0 0 6 0 4 0 0 0 0 0 | 0 0 0 4 1 0 0 0 0 0 0 | * * * 30 * * * * * * | 0 1 1 1 0 0 0 | 1 1 1 0
... ... .x.3.o.3.o.3.o. ♦ 0 5 0 | 0 0 0 10 0 0 | 0 0 0 0 0 10 0 0 0 0 0 | 0 0 0 0 5 0 0 0 0 0 0 | * * * * 3 * * * * * | 0 0 0 2 0 0 1 | 0 1 2 0
.oo3.xo ... .ox ... ...&#x ♦ 0 3 2 | 0 0 3 0 6 1 | 0 0 0 0 1 0 6 0 3 0 0 | 0 0 0 0 0 2 3 0 0 0 0 | * * * * * 30 * * * * | 1 0 0 0 2 0 0 | 2 0 0 1
... .xo ... .ox3.oo ...&#x ♦ 0 2 3 | 0 0 1 0 6 3 | 0 0 0 0 0 0 3 0 6 0 1 | 0 0 0 0 0 0 3 0 2 0 0 | * * * * * * 60 * * * | 0 0 1 0 1 1 0 | 1 0 1 1
... ... .xo3.ox3.oo ...&#x ♦ 0 4 6 | 0 0 0 6 12 12 | 0 0 0 0 0 4 0 6 12 4 4 | 0 0 0 0 1 0 0 4 4 1 0 | * * * * * * * 15 * * | 0 0 2 0 0 0 1 | 1 0 2 0
... ... ... .ox3.oo3.oo&#x ♦ 0 1 4 | 0 0 0 0 4 6 | 0 0 0 0 0 0 0 0 6 0 4 | 0 0 0 0 0 0 0 0 4 0 1 | * * * * * * * * 15 * | 0 0 0 0 0 2 1 | 0 0 2 1
... ... ..o3..x3..o3..o ♦ 0 0 10 | 0 0 0 0 0 30 | 0 0 0 0 0 0 0 0 0 10 20 | 0 0 0 0 0 0 0 0 0 5 5 | * * * * * * * * * 1 | 0 0 0 0 0 0 3 | 0 0 3 0
----------------------------+---------+------------------+--------------------------------+-------------------------------+-----------------------------+--------------------+--------
xoo3oxo oxo3oox ... ...&#xt ♦ 3 9 3 | 3 18 9 9 18 3 | 1 9 9 18 3 3 18 9 9 1 0 | 3 9 9 6 0 6 9 3 0 0 0 | 3 3 3 0 0 3 0 0 0 0 | 10 * * * * * * | 2 0 0 0
xo. ... ox.3oo.3oo. ...&#x ♦ 2 4 0 | 1 8 0 6 0 0 | 0 4 0 12 0 4 0 0 0 0 0 | 0 6 0 8 1 0 0 0 0 0 0 | 0 4 0 2 0 0 0 0 0 0 | * 15 * * * * * | 1 1 0 0
... oxo oxo3oox3ooo ...&#xt ♦ 1 8 6 | 0 8 4 12 24 12 | 0 0 4 12 0 8 12 12 24 4 4 | 0 0 6 8 2 0 12 8 8 1 0 | 0 0 4 2 0 0 4 2 0 0 | * * 15 * * * * | 1 0 1 0
... ... ox.3oo.3oo.3oo.&#x ♦ 1 5 0 | 0 5 0 10 0 0 | 0 0 0 10 0 10 0 0 0 0 0 | 0 0 0 10 5 0 0 0 0 0 0 | 0 0 0 5 1 0 0 0 0 0 | * * * 6 * * * | 0 1 1 0
.oo3.xo ... .ox3.oo ...&#x ♦ 0 3 3 | 0 0 3 0 9 3 | 0 0 0 0 1 0 9 0 9 0 1 | 0 0 0 0 0 3 9 0 3 0 0 | 0 0 0 0 0 3 3 0 0 0 | * * * * 20 * * | 1 0 0 1
... .xo ... .ox3.oo3.oo&#x ♦ 0 2 4 | 0 0 1 0 8 6 | 0 0 0 0 0 0 4 0 12 0 4 | 0 0 0 0 0 0 6 0 8 0 1 | 0 0 0 0 0 0 4 0 2 0 | * * * * * 15 * | 0 0 1 1
... ... .xo3.ox3.oo3.oo&#x ♦ 0 5 10 | 0 0 0 10 20 30 | 0 0 0 0 0 10 0 10 30 10 20 | 0 0 0 0 5 0 0 10 20 5 5 | 0 0 0 0 1 0 0 5 5 1 | * * * * * * 3 | 0 0 2 0
----------------------------+---------+------------------+--------------------------------+-------------------------------+-----------------------------+--------------------+--------
xoo3oxo oxo3oox3ooo ...&#xt ♦ 3 12 6 | 3 24 12 18 36 12 | 1 12 12 36 4 12 36 18 36 4 4 | 4 18 18 24 3 12 36 12 12 1 0 | 6 12 12 6 0 12 12 3 0 0 | 4 3 3 0 4 0 0 | 5 * * *
xo. ... ox.3oo.3oo.3oo.&#x ♦ 2 5 0 | 1 10 0 10 0 0 | 0 5 0 20 0 10 0 0 0 0 0 | 0 10 0 20 5 0 0 0 0 0 0 | 0 10 0 10 1 0 0 0 0 0 | 0 5 0 2 0 0 0 | * 3 * *
... oxo oxo3oox3ooo3ooo&#xt ♦ 1 10 10 | 0 10 5 20 40 30 | 0 0 5 20 0 20 20 20 60 10 20 | 0 0 10 20 10 0 30 20 40 5 5 | 0 0 10 10 2 0 20 10 10 1 | 0 0 5 2 0 5 2 | * * 3 *
.oo3.xo ... .ox3.oo3.oo&#x ♦ 0 3 4 | 0 0 3 0 12 6 | 0 0 0 0 1 0 12 0 18 0 4 | 0 0 0 0 0 4 18 0 12 0 1 | 0 0 0 0 0 6 12 0 3 0 | 0 0 0 0 4 3 0 | * * * 5
oxo3xoo3ooo oxo3oox3ooo&#xt → both heights = 1/2
(oct || pseudo tetdip || ortho oct)
o..3o..3o.. o..3o..3o.. & | 12 * ♦ 4 8 0 | 2 2 4 16 12 0 | 1 8 6 8 24 8 0 | 4 16 12 16 2 | 7 8 8 4 | 6 2
.o.3.o.3.o. .o.3.o.3.o. | * 16 ♦ 0 6 6 | 0 0 6 6 18 6 | 0 6 9 2 18 18 2 | 2 18 6 18 6 | 6 9 6 6 | 6 2
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
... x.. ... ... ... ... & | 2 0 | 24 * * | 1 1 0 4 0 0 | 1 4 0 4 6 0 0 | 4 6 6 4 0 | 6 4 4 1 | 5 1
oo.3oo.3oo. oo.3oo.3oo.&#x & | 1 1 | * 96 * | 0 0 1 2 3 0 | 0 2 3 1 6 3 0 | 1 9 3 6 1 | 4 6 3 2 | 5 1
.x. ... ... ... ... ... & | 0 2 | * * 48 | 0 0 1 0 3 2 | 0 2 3 0 3 6 1 | 1 9 1 6 3 | 4 6 2 3 | 5 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
o..3x.. ... ... ... ... & | 3 0 | 3 0 0 | 8 * * * * * ♦ 1 4 0 0 0 0 0 | 4 6 0 0 0 | 6 4 0 0 | 5 0
... x..3o.. ... ... ... & | 3 0 | 3 0 0 | * 8 * * * * | 1 0 0 4 0 0 0 | 4 0 6 0 0 | 6 0 4 0 | 4 1
ox. ... ... ... ... ...&#x & | 1 2 | 0 2 1 | * * 48 * * * ♦ 0 2 3 0 0 0 0 | 1 9 0 0 0 | 4 6 0 0 | 5 0
... xo. ... ... ... ...&#x & | 2 1 | 1 2 0 | * * * 96 * * | 0 1 0 1 3 0 0 | 1 3 3 3 0 | 3 3 3 1 | 4 1
... ... ... ox. ... ...&#x & | 1 2 | 0 2 1 | * * * * 144 * | 0 0 1 0 2 2 0 | 0 4 1 4 1 | 2 3 2 2 | 4 1
.x.3.o. ... ... ... ... & | 0 3 | 0 0 3 | * * * * * 32 | 0 1 0 0 0 3 1 | 1 3 0 3 3 | 3 3 1 3 | 4 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
o..3x..3o.. ... ... ... & ♦ 6 0 | 12 0 0 | 4 4 0 0 0 0 | 2 * * * * * * ♦ 4 0 0 0 0 | 6 0 0 0 | 4 0
ox.3xo. ... ... ... ...&#x & ♦ 3 3 | 3 6 3 | 1 0 3 3 0 1 | * 32 * * * * * ♦ 1 3 0 0 0 | 3 3 0 0 | 4 0
oxo ... ... oxo ... ...&#xt ♦ 2 4 | 0 8 4 | 0 0 4 0 4 0 | * * 36 * * * * ♦ 0 4 0 0 0 | 2 4 0 0 | 4 0
... xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 | 0 1 0 3 0 0 | * * * 32 * * * | 1 0 3 0 0 | 3 0 3 0 | 3 1
... xo. ... ox. ... ...&#x & ♦ 2 2 | 1 4 1 | 0 0 0 2 2 0 | * * * * 144 * * | 0 1 1 2 0 | 1 2 2 1 | 3 1
... ... ... ox.3oo. ...&#x & ♦ 1 3 | 0 3 3 | 0 0 0 0 3 1 | * * * * * 96 * | 0 1 0 2 1 | 1 2 1 2 | 3 1
.x.3.o.3.o. ... ... ... & ♦ 0 4 | 0 0 6 | 0 0 0 0 0 4 | * * * * * * 8 | 1 0 0 0 3 | 3 0 0 3 | 3 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
ox.3xo.3oo. ... ... ...&#x & ♦ 6 4 | 12 12 6 | 4 4 6 12 0 4 | 1 4 0 4 0 0 1 | 8 * * * * | 3 0 0 0 | 3 0
oxo3xoo ... oxo ... ...&#xt & ♦ 4 6 | 3 18 9 | 1 0 9 6 12 2 | 0 2 3 0 3 2 0 | * 48 * * * | 1 2 0 0 | 3 0
... xo.3oo. ox. ... ...&#x & ♦ 3 2 | 3 6 1 | 0 1 0 6 3 0 | 0 0 0 2 3 0 0 | * * 48 * * | 1 0 2 0 | 2 1
... xo. ... ox.3oo. ...&#x & ♦ 2 3 | 1 6 3 | 0 0 0 3 6 1 | 0 0 0 0 3 2 0 | * * * 96 * | 0 1 1 1 | 2 1
... ... ... ox.3oo.3oo.&#x & ♦ 1 4 | 0 4 6 | 0 0 0 0 6 4 | 0 0 0 0 0 4 1 | * * * * 24 | 1 0 0 2 | 2 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
oxo3xoo3ooo oxo ... ...&#xt & ♦ 7 8 | 12 32 16 | 4 4 16 24 24 8 | 1 8 6 8 12 8 2 | 2 4 4 0 2 | 12 * * * | 2 0
oxo3xoo ... oxo3oox ...&#xt ♦ 6 9 | 6 36 18 | 2 0 18 18 36 6 | 0 6 9 0 18 12 0 | 0 6 0 6 0 | * 16 * * | 2 0
... xo.3oo. ox.3oo. ...&#x & ♦ 3 3 | 3 9 3 | 0 1 0 9 9 1 | 0 0 0 3 9 3 0 | 0 0 3 3 0 | * * 32 * | 1 1
... xo. ... ox.3oo.3oo.&#x & ♦ 2 4 | 1 8 6 | 0 0 0 4 12 4 | 0 0 0 0 6 8 1 | 0 0 0 4 2 | * * * 24 | 1 1
------------------------------+-------+----------+------------------+---------------------+---------------+-------------+----
oxo3xoo3ooo oxo3oox ...&#xt & ♦ 9 12 | 15 60 30 | 5 4 30 48 72 16 | 1 16 18 12 54 36 3 | 3 18 12 24 6 | 3 4 4 3 | 8 *
... xo.3oo. ox.3oo.3oo.&#x & ♦ 3 4 | 3 12 6 | 0 1 0 12 18 4 | 0 0 0 4 18 12 1 | 0 0 6 12 3 | 0 0 4 3 | * 8