Acronym | octpy || octaco |
Name |
1/4-lune of rectified triacontiditeron, octahedron-pyramid atop octhedron-first-rotunda-of-icositetrachoron |
Circumradius | 1 |
Lace city in approx. ASCII-art |
_ +-------- o o3o4o (pt) _ - _ +----- x x3o4o (ope) _ - _ - _ +-- o o3x4o (co) o3o4o x3o4o -- ox3oo4oo&#x (octpy) x3o4o o3x4o -- xo3ox4oo&#x (octaco) |
Face vector | 25, 114, 156, 83, 18 |
Confer |
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Incidence matrix according to Dynkin symbol
oxo oxo3oox4ooo&#xt → both heights = 1/2 (pt || pseudo ope || co) o.. o..3o..4o.. | 1 * * ♦ 12 0 0 0 0 | 6 24 0 0 0 0 0 0 | 12 16 0 0 0 0 0 | 8 2 0 0 .o. .o.3.o.4.o. | * 12 * | 1 1 4 4 0 | 1 4 4 4 4 4 0 0 | 4 4 1 4 4 1 0 | 4 1 1 1 ..o ..o3..o4..o | * * 12 | 0 0 0 4 4 | 0 0 0 2 2 8 2 2 | 1 0 0 4 4 4 1 | 2 0 2 2 --------------------+---------+---------------+----------------------+--------------------+-------- oo. oo.3oo.4oo.&#x | 1 1 0 | 12 * * * * ♦ 1 4 0 0 0 0 0 0 | 4 4 0 0 0 0 0 | 4 1 0 0 .x. ... ... ... | 0 2 0 | * 6 * * * ♦ 1 0 0 4 0 0 0 0 | 4 0 0 4 0 0 0 | 4 0 1 0 ... .x. ... ... | 0 2 0 | * * 24 * * | 0 1 2 0 1 0 0 0 | 1 2 1 0 2 0 0 | 2 1 0 1 .oo .oo3.oo4.oo&#x | 0 1 1 | * * * 48 * | 0 0 0 1 1 2 0 0 | 1 0 0 2 2 1 0 | 2 0 1 1 ... ... ..x ... | 0 0 2 | * * * * 24 | 0 0 0 0 0 2 1 1 | 0 0 0 1 2 2 1 | 1 0 1 2 --------------------+---------+---------------+----------------------+--------------------+-------- ox. ... ... ...&#x | 1 2 0 | 2 1 0 0 0 | 6 * * * * * * * | 4 0 0 0 0 0 0 | 4 0 0 0 ... ox. ... ...&#x | 1 2 0 | 2 0 1 0 0 | * 24 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 ... .x.3.o. ... | 0 3 0 | 0 0 3 0 0 | * * 16 * * * * * | 0 1 1 0 1 0 0 | 1 1 0 1 .xo ... ... ...&#x | 0 2 1 | 0 1 0 2 0 | * * * 24 * * * * | 1 0 0 2 0 0 0 | 2 0 1 0 ... .xo ... ...&#x | 0 2 1 | 0 0 1 2 0 | * * * * 24 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 ... ... .ox ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 48 * * | 0 0 0 1 1 1 0 | 1 0 1 1 ... ..o3..x ... | 0 0 3 | 0 0 0 0 3 | * * * * * * 8 * | 0 0 0 0 2 0 1 | 1 0 0 2 ... ... ..x4..o | 0 0 4 | 0 0 0 0 4 | * * * * * * * 6 | 0 0 0 0 0 2 1 | 0 0 1 2 --------------------+---------+---------------+----------------------+--------------------+-------- oxo oxo ... ...&#xt ♦ 1 4 1 | 4 2 2 4 0 | 2 2 0 2 2 0 0 0 | 12 * * * * * * | 2 0 0 0 ... ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3 0 0 | 0 3 1 0 0 0 0 0 | * 16 * * * * * | 1 1 0 0 ... .x.3.o.4.o. ♦ 0 6 0 | 0 0 12 0 0 | 0 0 8 0 0 0 0 0 | * * 2 * * * * | 0 1 0 1 .xo ... .ox ...&#x ♦ 0 2 2 | 0 1 0 4 1 | 0 0 0 2 0 2 0 0 | * * * 24 * * * | 1 0 1 0 ... .xo3.ox ...&#x ♦ 0 3 3 | 0 0 3 6 3 | 0 0 1 0 3 3 1 0 | * * * * 16 * * | 1 0 0 1 ... ... .ox4.oo&#x ♦ 0 1 4 | 0 0 0 4 4 | 0 0 0 0 0 4 0 1 | * * * * * 12 * | 0 0 1 1 ... ..o3..x4.o ♦ 0 0 12 | 0 0 0 0 24 | 0 0 0 0 0 0 8 6 | * * * * * * 1 | 0 0 0 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 | 8 * * * ... ox.3oo.4oo.&#x ♦ 1 6 0 | 6 0 12 0 0 | 0 12 8 0 0 0 0 0 | 0 8 1 0 0 0 0 | * 2 * * .xo ... .ox4.oo&#x ♦ 0 2 4 | 0 1 0 8 4 | 0 0 0 4 0 8 0 1 | 0 0 0 4 0 2 0 | * * 6 * ... .xo3.ox4.oo&#x ♦ 0 6 12 | 0 0 12 24 24 | 0 0 8 0 12 24 8 6 | 0 0 1 0 8 6 1 | * * * 2
ox3oo4oo&#x || xo3ox4oo&#x → height = 1/sqrt(2) = 0.707107
(octpy || octaco)
o.3o.4o. .. .. .. | 1 * * * ♦ 6 6 0 0 0 0 0 0 | 12 6 12 0 0 0 0 0 0 0 0 0 | 8 12 8 0 0 0 0 0 0 0 0 | 1 8 1 0 0 0
.o3.o4.o .. .. .. | * 6 * * | 1 0 4 1 4 0 0 0 | 4 1 0 4 4 4 4 0 0 0 0 0 | 4 4 0 1 4 4 1 0 0 0 0 | 1 4 0 1 1 0
.. .. .. o.3o.4o. | * * 6 * | 0 1 0 1 0 4 4 0 | 0 1 4 0 0 4 0 4 4 4 0 0 | 0 4 4 0 0 4 0 1 4 1 0 | 0 4 1 0 1 1
.. .. .. .o3.o4.o | * * * 12 | 0 0 0 0 2 0 2 4 | 0 0 0 0 1 2 4 0 1 4 2 2 | 0 1 0 0 2 4 2 0 2 2 1 | 0 2 0 1 2 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
oo3oo4oo&#x .. .. .. | 1 1 0 0 | 6 * * * * * * * ♦ 4 1 0 0 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 | 1 4 0 0 0 0
o.3o.4o. || o.3o.4o. | 1 0 1 0 | * 6 * * * * * * ♦ 0 1 4 0 0 0 0 0 0 0 0 0 | 0 4 4 0 0 0 0 0 0 0 0 | 0 4 1 0 0 0
.x .. .. .. .. .. | 0 2 0 0 | * * 12 * * * * * | 1 0 0 2 1 0 0 0 0 0 0 0 | 2 1 0 1 2 0 0 0 0 0 0 | 1 2 0 1 0 0
.o3.o4.o || o.3o.4o. | 0 1 1 0 | * * * 6 * * * * ♦ 0 1 0 0 0 4 0 0 0 0 0 0 | 0 4 0 0 0 4 0 0 0 0 0 | 0 4 0 0 1 0
.o3.o4.o || .o3.o4.o | 0 1 0 1 | * * * * 24 * * * | 0 0 0 0 1 1 2 0 0 0 0 0 | 0 1 0 0 2 2 1 0 0 0 0 | 0 2 0 1 1 0
.. .. .. x. .. .. | 0 0 2 0 | * * * * * 12 * * | 0 0 1 0 0 0 0 2 1 0 0 0 | 0 1 2 0 0 0 0 1 2 0 0 | 0 2 1 0 0 1
.. .. .. oo3oo4oo&#x | 0 0 1 1 | * * * * * * 24 * | 0 0 0 0 0 1 0 0 1 2 0 0 | 0 1 0 0 0 2 0 0 2 1 0 | 0 2 0 0 1 1
.. .. .. .. .x .. | 0 0 0 2 | * * * * * * * 24 | 0 0 0 0 0 0 1 0 0 1 1 1 | 0 0 0 0 1 1 1 0 1 1 1 | 0 1 0 1 1 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
ox .. ..&#x .. .. .. | 1 2 0 0 | 2 0 1 0 0 0 0 0 | 12 * * * * * * * * * * * | 2 1 0 0 0 0 0 0 0 0 0 | 1 2 0 0 0 0
oo3oo4oo&#x || o.3o.4o. | 1 1 1 0 | 1 1 0 1 0 0 0 0 | * 6 * * * * * * * * * * | 0 4 0 0 0 0 0 0 0 0 0 | 0 4 0 0 0 0
o.3o.4o. || x. .. .. | 1 0 2 0 | 0 2 0 0 0 1 0 0 | * * 12 * * * * * * * * * | 0 1 2 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0
.x3.o .. .. .. .. | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * * 8 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 0 | 1 1 0 1 0 0
.x .. .. || .o3.o4.o | 0 2 0 1 | 0 0 1 0 2 0 0 0 | * * * * 12 * * * * * * * | 0 1 0 0 2 0 0 0 0 0 0 | 0 2 0 1 0 0
.o3.o4.o || oo3oo4oo&#x | 0 1 1 1 | 0 0 0 1 1 0 1 0 | * * * * * 24 * * * * * * | 0 1 0 0 0 2 0 0 0 0 0 | 0 2 0 0 1 0
.o3.o4.o || .. .x .. | 0 1 0 2 | 0 0 0 0 2 0 0 1 | * * * * * * 24 * * * * * | 0 0 0 0 1 1 1 0 0 0 0 | 0 1 0 1 1 0
.. .. .. x.3o. .. | 0 0 3 0 | 0 0 0 0 0 3 0 0 | * * * * * * * 8 * * * * | 0 0 1 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.. .. .. xo .. ..&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * 12 * * * | 0 1 0 0 0 0 0 0 2 0 0 | 0 2 0 0 0 1
.. .. .. .. ox ..&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * * 24 * * | 0 0 0 0 0 1 0 0 1 1 0 | 0 1 0 0 1 1
.. .. .. .o3.x .. | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * 8 * | 0 0 0 0 1 0 0 0 1 0 1 | 0 1 0 1 0 1
.. .. .. .. .x4.o | 0 0 0 4 | 0 0 0 0 0 0 0 4 | * * * * * * * * * * * 6 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
ox3oo ..&#x .. .. .. ♦ 1 3 0 0 | 3 0 3 0 0 0 0 0 | 3 0 0 1 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * | 1 1 0 0 0 0
ox .. ..&#x || xo .. ..&#x ♦ 1 2 2 1 | 2 2 1 2 2 1 2 0 | 1 2 1 0 1 2 0 0 1 0 0 0 | * 12 * * * * * * * * * | 0 2 0 0 0 0
o.3o.4o. || x.3o. .. ♦ 1 0 3 0 | 0 3 0 0 0 3 0 0 | 0 0 3 0 0 0 0 1 0 0 0 0 | * * 8 * * * * * * * * | 0 1 1 0 0 0
.x3.o4.o .. .. .. ♦ 0 6 0 0 | 0 0 12 0 0 0 0 0 | 0 0 0 8 0 0 0 0 0 0 0 0 | * * * 1 * * * * * * * | 1 0 0 1 0 0
.x3.o .. || .o3.x .. ♦ 0 3 0 3 | 0 0 3 0 6 0 0 3 | 0 0 0 1 3 0 3 0 0 0 1 0 | * * * * 8 * * * * * * | 0 1 0 1 0 0
.o3.o4.o || .. ox ..&#x ♦ 0 1 1 2 | 0 0 0 1 2 0 2 1 | 0 0 0 0 0 2 1 0 0 1 0 0 | * * * * * 24 * * * * * | 0 1 0 0 1 0
.o3.o4.o || .. .x4.o ♦ 0 1 0 4 | 0 0 0 0 4 0 0 4 | 0 0 0 0 0 0 4 0 0 0 0 1 | * * * * * * 6 * * * * | 0 0 0 1 1 0
.. .. .. x.3o.4o. ♦ 0 0 6 0 | 0 0 0 0 0 12 0 0 | 0 0 0 0 0 0 0 8 0 0 0 0 | * * * * * * * 1 * * * | 0 0 1 0 0 1
.. .. .. xo3ox ..&#x ♦ 0 0 3 3 | 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 0 1 3 3 1 0 | * * * * * * * * 8 * * | 0 1 0 0 0 1
.. .. .. .. ox4oo&#x ♦ 0 0 1 4 | 0 0 0 0 0 0 4 4 | 0 0 0 0 0 0 0 0 0 4 0 1 | * * * * * * * * * 6 * | 0 0 0 0 1 1
.. .. .. .o3.x4.o ♦ 0 0 0 12 | 0 0 0 0 0 0 0 24 | 0 0 0 0 0 0 0 0 0 0 8 6 | * * * * * * * * * * 1 | 0 0 0 1 0 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
ox3oo4oo&#x .. .. .. ♦ 1 6 0 0 | 6 0 12 0 0 0 0 0 | 12 0 0 8 0 0 0 0 0 0 0 0 | 8 0 0 1 0 0 0 0 0 0 0 | 1 * * * * *
ox3oo ..&#x || xo3ox ..&#x ♦ 1 3 3 3 | 3 3 3 3 6 3 6 3 | 3 3 3 1 3 6 3 1 3 3 1 0 | 1 3 1 0 1 3 0 0 1 0 0 | * 8 * * * *
o.3o.4o. || x.3o.4o. ♦ 1 0 6 0 | 0 6 0 0 0 12 0 0 | 0 0 12 0 0 0 0 8 0 0 0 0 | 0 0 8 0 0 0 0 1 0 0 0 | * * 1 * * *
.x3.o4.o || .o3.x4.o ♦ 0 6 0 12 | 0 0 12 0 24 0 0 24 | 0 0 0 8 12 0 24 0 0 0 8 6 | 0 0 0 1 8 0 6 0 0 0 1 | * * * 1 * *
.o3.o4.o || .. ox4oo&#x ♦ 0 1 1 4 | 0 0 0 1 4 0 4 4 | 0 0 0 0 0 4 4 0 0 4 0 1 | 0 0 0 0 0 4 1 0 0 1 0 | * * * * 6 *
.. .. .. xo3ox4oo&#x ♦ 0 0 6 12 | 0 0 0 0 0 12 24 24 | 0 0 0 0 0 0 0 8 12 24 8 6 | 0 0 0 0 0 0 0 1 8 6 1 | * * * * * 1
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