Acronym | octpyp, line||ope |
Name |
octahedron-prismatic wedge, line atop ope, octahedral-pyramid prism, half of hexip |
Circumradius | sqrt(3)/2 = 0.866025 |
Lace city in approx. ASCII-art |
o3o x x3o x o3x x |
o3o4o o3o4o x3o4o x3o4o | |
Face vector | 14, 43, 58, 38, 11 |
Confer |
|
Incidence matrix according to Dynkin symbol
xx ox3oo4oo&#x → height = 1/sqrt(2) = 0.707107
(line || ope)
o. o.3o.4o. | 2 * | 1 6 0 0 | 6 12 0 0 | 12 8 0 0 | 8 1 0
.o .o3.o4.o | * 12 | 0 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1
---------------+------+-----------+------------+-----------+------
x. .. .. .. | 2 0 | 1 * * * ♦ 6 0 0 0 | 12 0 0 0 | 8 0 0
oo oo3oo4oo&#x | 1 1 | * 12 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0
.x .. .. .. | 0 2 | * * 6 * ♦ 1 0 4 0 | 4 0 4 0 | 4 0 1
.. .x .. .. | 0 2 | * * * 24 | 0 1 1 2 | 1 2 2 1 | 2 1 1
---------------+------+-----------+------------+-----------+------
xx .. .. ..&#x | 2 2 | 1 2 1 0 | 6 * * * | 4 0 0 0 | 4 0 0
.. ox .. ..&#x | 1 2 | 0 2 0 1 | * 24 * * | 1 2 0 0 | 2 1 0
.x .x .. .. | 0 4 | 0 0 2 2 | * * 12 * | 1 0 2 0 | 2 0 1
.. .x3.o .. | 0 3 | 0 0 0 3 | * * * 16 | 0 1 1 1 | 1 1 1
---------------+------+-----------+------------+-----------+------
xx ox .. ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 12 * * * | 2 0 0
.. ox3oo ..&#x ♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 16 * * | 1 1 0
.x .x3.o .. ♦ 0 6 | 0 0 3 6 | 0 0 3 2 | * * 8 * | 1 0 1
.. .x3.o4.o ♦ 0 6 | 0 0 0 12 | 0 0 0 8 | * * * 2 | 0 1 1
---------------+------+-----------+------------+-----------+------
xx ox3oo ..&#x ♦ 2 6 | 1 6 3 6 | 3 6 3 2 | 3 2 1 0 | 8 * *
.. ox3oo4oo&#x ♦ 1 6 | 0 6 0 12 | 0 12 0 8 | 0 8 0 1 | * 2 *
.x .x3.o4.o ♦ 0 12 | 0 0 6 24 | 0 0 12 16 | 0 0 8 2 | * * 1
xx oo3ox3oo&#x → height = 1/sqrt(2) = 0.707107
(line || ope)
o. o.3o.3o. | 2 * | 1 6 0 0 | 6 12 0 0 0 | 12 4 4 0 0 0 | 4 4 1 0
.o .o3.o3.o | * 12 | 0 1 1 4 | 1 4 4 2 2 | 4 2 2 2 2 1 | 2 2 1 1
---------------+------+-----------+-------------+--------------+--------
x. .. .. .. | 2 0 | 1 * * * ♦ 6 0 0 0 0 | 12 0 0 0 0 0 | 4 4 0 0
oo oo3oo3oo&#x | 1 1 | * 12 * * | 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0
.x .. .. .. | 0 2 | * * 6 * ♦ 1 0 4 0 0 | 4 0 0 2 2 0 | 2 2 0 1
.. .. .x .. | 0 2 | * * * 24 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1
---------------+------+-----------+-------------+--------------+--------
xx .. .. ..&#x | 2 2 | 1 2 1 0 | 6 * * * * | 4 0 0 0 0 0 | 2 2 0 0
.. .. ox ..&#x | 1 2 | 0 2 0 1 | * 24 * * * | 1 1 1 0 0 0 | 1 1 1 0
.x .. .x .. | 0 4 | 0 0 2 2 | * * 12 * * | 1 0 0 1 1 0 | 1 1 0 1
.. .o3.x .. | 0 3 | 0 0 0 3 | * * * 8 * | 0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.o | 0 3 | 0 0 0 3 | * * * * 8 | 0 0 1 0 1 1 | 0 1 1 1
---------------+------+-----------+-------------+--------------+--------
xx .. ox ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 0 | 12 * * * * * | 1 1 0 0
.. oo3ox ..&#x ♦ 1 3 | 0 3 0 3 | 0 3 0 1 0 | * 8 * * * * | 1 0 1 0
.. .. ox3oo&#x ♦ 1 3 | 0 3 0 3 | 0 3 0 0 1 | * * 8 * * * | 0 1 1 0
.x .o3.x .. ♦ 0 6 | 0 0 3 6 | 0 0 3 2 0 | * * * 4 * * | 1 0 0 1
.x .. .x3.o ♦ 0 6 | 0 0 3 6 | 0 0 3 0 2 | * * * * 4 * | 0 1 0 1
.. .o3.x3.o ♦ 0 6 | 0 0 0 12 | 0 0 0 4 4 | * * * * * 2 | 0 0 1 1
---------------+------+-----------+-------------+--------------+--------
xx oo3ox ..&#x ♦ 2 6 | 1 6 3 6 | 3 6 3 2 0 | 3 2 0 1 0 0 | 4 * * *
xx .. ox3oo&#x ♦ 2 6 | 1 6 3 6 | 3 6 3 0 2 | 3 0 2 0 1 0 | * 4 * *
.. oo3ox3oo&#x ♦ 1 6 | 0 6 0 12 | 0 12 0 4 4 | 0 4 4 0 0 1 | * * 2 *
.x .o3.x3.o ♦ 0 12 | 0 0 6 24 | 0 0 12 8 8 | 0 0 0 4 4 2 | * * * 1
xxx oox3oxo&#x → height(1,2) = height(1,3) = height(2,3) = sqrt(2/3) = 0.816497 o.. o..3o.. | 2 * * | 1 3 3 0 0 0 0 0 | 3 3 6 3 3 0 0 0 0 0 0 0 | 3 1 6 3 3 3 1 0 0 0 0 0 | 1 3 3 1 1 0 .o. .o.3.o. | * 6 * | 0 1 0 1 2 2 0 0 | 1 2 2 0 0 2 1 2 1 2 0 0 | 2 1 2 1 2 0 0 1 1 2 1 0 | 1 1 2 1 0 1 ..o ..o3..o | * * 6 | 0 0 1 0 0 2 1 2 | 0 0 2 1 2 0 0 2 2 1 2 1 | 0 0 2 2 1 2 1 0 2 1 1 1 | 0 2 1 1 1 1 ---------------+-------+------------------+--------------------------+-------------------------+------------ x.. ... ... | 2 0 0 | 1 * * * * * * * ♦ 3 0 0 3 0 0 0 0 0 0 0 0 | 3 0 6 0 0 3 0 0 0 0 0 0 | 1 3 3 0 1 0 oo. oo.3oo.&#x | 1 1 0 | * 6 * * * * * * | 1 2 2 0 0 0 0 0 0 0 0 0 | 2 1 2 1 2 0 0 0 0 0 0 0 | 1 1 2 1 0 0 o.o o.o3o.o&#x | 1 0 1 | * * 6 * * * * * | 0 0 2 1 2 0 0 0 0 0 0 0 | 0 0 2 2 1 2 1 0 0 0 0 0 | 0 2 1 1 1 0 .x. ... ... | 0 2 0 | * * * 3 * * * * ♦ 1 0 0 0 0 2 0 2 0 0 0 0 | 2 0 2 0 0 0 0 1 1 2 0 0 | 1 1 2 0 0 1 ... ... .x. | 0 2 0 | * * * * 6 * * * | 0 1 0 0 0 1 1 0 0 1 0 0 | 1 1 0 0 1 0 0 1 0 1 1 0 | 1 0 1 1 0 1 .oo .oo3.oo&#x | 0 1 1 | * * * * * 12 * * | 0 0 1 0 0 0 0 1 1 1 0 0 | 0 0 1 1 1 0 0 0 1 1 1 0 | 0 1 1 1 0 1 ..x ... ... | 0 0 2 | * * * * * * 3 * ♦ 0 0 0 1 0 0 0 2 0 0 2 0 | 0 0 2 0 0 2 0 0 2 1 0 1 | 0 2 1 0 1 1 ... ..x ... | 0 0 2 | * * * * * * * 6 | 0 0 0 0 1 0 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 0 1 1 | 0 1 0 1 1 1 ---------------+-------+------------------+--------------------------+-------------------------+------------ xx. ... ...&#x | 2 2 0 | 1 2 0 1 0 0 0 0 | 3 * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0 ... ... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 0 | * 6 * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0 ooo ooo3ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 0 | * * 12 * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0 x.x ... ...&#x | 2 0 2 | 1 0 2 0 0 0 1 0 | * * * 3 * * * * * * * * | 0 0 2 0 0 2 0 0 0 0 0 0 | 0 2 1 0 1 0 ... o.x ...&#x | 1 0 2 | 0 0 2 0 0 0 0 1 | * * * * 6 * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 0 | 0 1 0 1 1 0 .x. ... .x. | 0 4 0 | 0 0 0 2 2 0 0 0 | * * * * * 3 * * * * * * | 1 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1 ... .o.3.x. | 0 3 0 | 0 0 0 0 3 0 0 0 | * * * * * * 2 * * * * * | 0 1 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1 .xx ... ...&#x | 0 2 2 | 0 0 0 1 0 2 1 0 | * * * * * * * 6 * * * * | 0 0 1 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1 ... .ox ...&#x | 0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * * * * 6 * * * | 0 0 0 1 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1 ... ... .xo&#x | 0 2 1 | 0 0 0 0 1 2 0 0 | * * * * * * * * * 6 * * | 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 0 1 ..x ..x ... | 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * * * 3 * | 0 0 0 0 0 1 0 0 1 0 0 1 | 0 1 0 0 1 1 ... ..x3..o | 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * * 2 | 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1 ---------------+-------+------------------+--------------------------+-------------------------+------------ xx. ... ox.&#x ♦ 2 4 0 | 1 4 0 2 2 0 0 0 | 2 2 0 0 0 1 0 0 0 0 0 0 | 3 * * * * * * * * * * * | 1 0 1 0 0 0 ... oo.3ox.&#x ♦ 1 3 0 | 0 3 0 0 3 0 0 0 | 0 3 0 0 0 0 1 0 0 0 0 0 | * 2 * * * * * * * * * * | 1 0 0 1 0 0 xxx ... ...&#x ♦ 2 2 2 | 1 2 2 1 0 2 1 0 | 1 0 2 1 0 0 0 1 0 0 0 0 | * * 6 * * * * * * * * * | 0 1 1 0 0 0 ... oox ...&#x ♦ 1 1 2 | 0 1 2 0 0 2 0 1 | 0 0 2 0 1 0 0 0 1 0 0 0 | * * * 6 * * * * * * * * | 0 1 0 1 0 0 ... ... oxo&#x ♦ 1 2 1 | 0 2 1 0 1 2 0 0 | 0 1 2 0 0 0 0 0 0 1 0 0 | * * * * 6 * * * * * * * | 0 0 1 1 0 0 x.x o.x ...&#x ♦ 2 0 4 | 1 0 4 0 0 0 2 2 | 0 0 0 2 2 0 0 0 0 0 1 0 | * * * * * 3 * * * * * * | 0 1 0 0 1 0 ... o.x3o.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 | * * * * * * 2 * * * * * | 0 0 0 1 1 0 .x. .o.3.x. ♦ 0 6 0 | 0 0 0 3 6 0 0 0 | 0 0 0 0 0 3 2 0 0 0 0 0 | * * * * * * * 1 * * * * | 1 0 0 0 0 1 .xx .ox ...&#x ♦ 0 2 4 | 0 0 0 1 0 4 2 2 | 0 0 0 0 0 0 0 2 2 0 1 0 | * * * * * * * * 3 * * * | 0 1 0 0 0 1 .xx ... .xo&#x ♦ 0 4 2 | 0 0 0 2 2 4 1 0 | 0 0 0 0 0 1 0 2 0 2 0 0 | * * * * * * * * * 3 * * | 0 0 1 0 0 1 ... .ox3.xo&#x ♦ 0 3 3 | 0 0 0 0 3 6 0 3 | 0 0 0 0 0 0 1 0 3 3 0 1 | * * * * * * * * * * 2 * | 0 0 0 1 0 1 ..x ..x3..o ♦ 0 0 6 | 0 0 0 0 0 0 3 6 | 0 0 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * 1 | 0 0 0 0 1 1 ---------------+-------+------------------+--------------------------+-------------------------+------------ xx. oo.3ox.&#x ♦ 2 6 0 | 1 6 0 3 6 0 0 0 | 3 6 0 0 0 3 2 0 0 0 0 0 | 3 2 0 0 0 0 0 1 0 0 0 0 | 1 * * * * * xxx oox ...&#x ♦ 2 2 4 | 1 2 4 1 0 4 2 2 | 1 0 4 2 2 0 0 2 2 0 1 0 | 0 0 2 2 0 1 0 0 1 0 0 0 | * 3 * * * * xxx ... oxo&#x ♦ 2 4 2 | 1 4 2 2 2 4 1 0 | 2 2 4 1 0 1 0 2 0 2 0 0 | 1 0 2 0 2 0 0 0 0 1 0 0 | * * 3 * * * ... oox3oxo&#x ♦ 1 3 3 | 0 3 3 0 3 6 0 3 | 0 3 6 0 3 0 1 0 3 3 0 1 | 0 1 0 3 3 0 1 0 0 0 1 0 | * * * 2 * * x.x o.x3o.o&#x ♦ 2 0 6 | 1 0 6 0 0 0 3 6 | 0 0 0 3 6 0 0 0 0 0 3 2 | 0 0 0 0 0 3 2 0 0 0 0 1 | * * * * 1 * .xx .ox3.xo&#x ♦ 0 6 6 | 0 0 0 3 6 12 3 6 | 0 0 0 0 0 3 2 6 6 6 3 2 | 0 0 0 0 0 0 0 1 3 3 2 1 | * * * * * 1
ooxx3oooo4oooo&#xr → height(1,2) = height(3,4) = 1 height(2,3) = height(1,4) = 1/sqrt(2) = 0.707107 o...3o...4o... | 1 * * * | 1 6 0 0 0 0 | 6 12 0 0 0 0 | 12 8 0 0 0 0 | 8 1 0 0 .o..3.o..4.o.. | * 1 * * | 1 0 6 0 0 0 | 6 0 12 0 0 0 | 12 0 8 0 0 0 | 8 0 1 0 ..o.3..o.4..o. | * * 6 * | 0 0 1 4 1 0 | 1 0 4 4 4 0 | 4 0 4 1 4 0 | 4 0 1 1 ...o3...o4...o | * * * 6 | 0 1 0 0 1 4 | 1 4 0 0 4 4 | 4 4 0 0 4 1 | 4 1 0 1 -------------------+---------+---------------+----------------+--------------+-------- oo..3oo..4oo..&#x | 1 1 0 0 | 1 * * * * * | 6 0 0 0 0 0 | 12 0 0 0 0 0 | 8 0 0 0 o..o3o..o4o..o&#x | 1 0 0 1 | * 6 * * * * | 1 4 0 0 0 0 | 4 4 0 0 0 0 | 4 1 0 0 .oo.3.oo.4.oo.&#x | 0 1 1 0 | * * 6 * * * | 1 0 4 0 0 0 | 4 0 4 0 0 0 | 4 0 1 0 ..x. .... .... | 0 0 2 0 | * * * 12 * * | 0 0 1 2 1 0 | 1 0 2 1 2 0 | 2 0 1 1 ..oo3..oo4..oo&#x | 0 0 1 1 | * * * * 6 * | 1 0 0 0 4 0 | 4 0 0 0 4 0 | 4 0 0 1 ...x .... .... | 0 0 0 2 | * * * * * 12 | 0 1 0 0 1 2 | 1 2 0 0 2 1 | 2 1 0 1 -------------------+---------+---------------+----------------+--------------+-------- oooo3oooo4oooo&#xr | 1 1 1 1 | 1 1 1 0 1 0 | 6 * * * * * | 4 0 0 0 0 0 | 4 0 0 0 o..x .... ....&#x | 1 0 0 2 | 0 2 0 0 0 1 | * 12 * * * * | 1 2 0 0 0 0 | 2 1 0 0 .ox. .... ....&#x | 0 1 2 0 | 0 0 2 1 0 0 | * * 12 * * * | 1 0 2 0 0 0 | 2 0 1 0 ..x.3..o. .... | 0 0 3 0 | 0 0 0 3 0 0 | * * * 8 * * | 0 0 1 1 1 0 | 1 0 1 1 ..xx .... ....&#x | 0 0 2 2 | 0 0 0 1 2 1 | * * * * 12 * | 1 0 0 0 2 0 | 2 0 0 1 ...x3...o .... | 0 0 0 3 | 0 0 0 0 0 3 | * * * * * 8 | 0 1 0 0 1 1 | 1 1 0 1 -------------------+---------+---------------+----------------+--------------+-------- ooxx .... ....&#xr ♦ 1 1 2 2 | 1 2 2 1 2 1 | 2 1 1 0 1 0 | 12 * * * * * | 2 0 0 0 o..x3o..o ....&#x ♦ 1 0 0 3 | 0 3 0 0 0 3 | 0 3 0 0 0 1 | * 8 * * * * | 1 1 0 0 .ox.3.oo. ....&#x ♦ 0 1 3 0 | 0 0 3 3 0 0 | 0 0 3 1 0 0 | * * 8 * * * | 1 0 1 0 ..x.3..o.4..o. ♦ 0 0 6 0 | 0 0 0 12 0 0 | 0 0 0 8 0 0 | * * * 1 * * | 0 0 1 1 ..xx3..oo ....&#x ♦ 0 0 3 3 | 0 0 0 3 3 3 | 0 0 0 1 3 1 | * * * * 8 * | 1 0 0 1 ...x3...o4...o ♦ 0 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 8 | * * * * * 1 | 0 1 0 1 -------------------+---------+---------------+----------------+--------------+-------- ooxx3oooo ....&#xr ♦ 1 1 3 3 | 1 3 3 3 3 3 | 3 3 3 1 3 1 | 3 1 1 0 1 0 | 8 * * * o..x3o..o4o..o&#x ♦ 1 0 0 6 | 0 6 0 0 0 12 | 0 12 0 0 0 8 | 0 8 0 0 0 1 | * 1 * * .ox.3.oo.4.oo.&#x ♦ 0 1 6 0 | 0 0 6 12 0 0 | 0 0 12 8 0 0 | 0 0 8 1 0 0 | * * 1 * ..xx3..oo4..oo&#x ♦ 0 0 6 6 | 0 0 0 12 6 12 | 0 0 0 8 12 8 | 0 0 0 1 8 1 | * * * 1
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