Acronym | opeaco |
Name |
octahedron-prism atop cuboctahedron, diminished 1/4-lune of rat |
Circumradius | 1 |
Lace city in approx. ASCII-art |
x3o4o x3o4o o3x4o |
x o3x x x3o o x3o o x3x o o3x | |
Face vector | 24, 102, 138, 75, 17 |
Confer |
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Incidence matrix according to Dynkin symbol
xo xo3ox4oo&#x → height = 1/2 o. o.3o.4o. | 12 * | 1 4 4 0 | 4 4 4 4 4 0 0 | 4 1 4 4 4 1 0 | 1 4 1 1 .o .o3.o4.o | * 12 | 0 0 4 4 | 0 0 2 2 8 2 2 | 0 0 1 4 4 4 1 | 0 2 2 2 ---------------+-------+------------+--------------------+-------------------+-------- x. .. .. .. | 2 0 | 6 * * * ♦ 4 0 4 0 0 0 0 | 4 0 4 4 0 0 0 | 1 4 1 0 .. x. .. .. | 2 0 | * 24 * * | 1 2 0 1 0 0 0 | 2 1 1 0 2 0 0 | 1 2 0 1 oo oo3oo4oo&#x | 1 1 | * * 48 * | 0 0 1 1 2 0 0 | 0 0 1 2 2 1 0 | 0 2 1 1 .. .. .x .. | 0 2 | * * * 24 | 0 0 0 0 2 1 1 | 0 0 0 1 2 2 1 | 0 1 1 2 ---------------+-------+------------+--------------------+-------------------+-------- x. x. .. .. | 4 0 | 2 2 0 0 | 12 * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0 .. x.3o. .. | 3 0 | 0 3 0 0 | * 16 * * * * * | 1 1 0 0 1 0 0 | 1 1 0 1 xo .. .. ..&#x | 2 1 | 1 0 2 0 | * * 24 * * * * | 0 0 1 2 0 0 0 | 0 2 1 0 .. xo .. ..&#x | 2 1 | 0 1 2 0 | * * * 24 * * * | 0 0 1 0 2 0 0 | 0 2 0 1 .. .. ox ..&#x | 1 2 | 0 0 2 1 | * * * * 48 * * | 0 0 0 1 1 1 0 | 0 1 1 1 .. .o3.x .. | 0 3 | 0 0 0 3 | * * * * * 8 * | 0 0 0 0 2 0 1 | 0 1 0 2 .. .. .x4.o | 0 4 | 0 0 0 4 | * * * * * * 6 | 0 0 0 0 0 2 1 | 0 0 1 2 ---------------+-------+------------+--------------------+-------------------+-------- x. x.3o. .. ♦ 6 0 | 3 6 0 0 | 3 2 0 0 0 0 0 | 8 * * * * * * | 1 1 0 0 .. x.3o.4o. ♦ 6 0 | 0 12 0 0 | 0 8 0 0 0 0 0 | * 2 * * * * * | 1 0 0 1 xo xo .. ..&#x ♦ 4 1 | 2 2 4 0 | 1 0 2 2 0 0 0 | * * 12 * * * * | 0 2 0 0 xo .. ox ..&#x ♦ 2 2 | 1 0 4 1 | 0 0 2 0 2 0 0 | * * * 24 * * * | 0 1 1 0 .. xo3ox ..&#x ♦ 3 3 | 0 3 6 3 | 0 1 0 3 3 1 0 | * * * * 16 * * | 0 1 0 1 .. .. ox4oo&#x ♦ 1 4 | 0 0 4 4 | 0 0 0 0 4 0 1 | * * * * * 12 * | 0 0 1 1 .. .o3.x4o ♦ 0 12 | 0 0 0 24 | 0 0 0 0 0 8 6 | * * * * * * 1 | 0 0 0 2 ---------------+-------+------------+--------------------+-------------------+-------- x. x.3o.4o. ♦ 12 0 | 6 24 0 0 | 12 16 0 0 0 0 0 | 8 2 0 0 0 0 0 | 1 * * * xo xo3ox ..&#x ♦ 6 3 | 3 6 12 3 | 3 2 6 6 6 1 0 | 1 0 3 3 2 0 0 | * 8 * * xo .. ox4oo&#x ♦ 2 4 | 1 0 8 4 | 0 0 4 0 8 0 1 | 0 0 0 4 0 2 0 | * * 6 * .. xo3ox4oo&#x ♦ 6 12 | 0 12 24 24 | 0 8 0 12 24 8 6 | 0 1 0 0 8 6 1 | * * * 2
xo ox3xo3ox&#x → height = 1/2 o. o.3o.3o. | 12 * | 1 4 4 0 0 | 4 2 2 4 2 4 2 0 0 0 | 2 2 1 2 4 2 2 1 2 0 | 1 2 1 2 1 .o .o3.o3.o | * 12 | 0 0 4 2 2 | 0 0 0 2 4 2 4 1 2 1 | 0 0 0 2 1 2 2 4 2 1 | 0 1 2 1 2 ---------------+-------+---------------+--------------------------+-------------------------+---------- x. .. .. .. | 2 0 | 6 * * * * ♦ 4 0 0 4 0 0 0 0 0 0 | 2 2 0 2 4 2 0 0 0 0 | 1 2 1 2 0 .. .. x. .. | 2 0 | * 24 * * * | 1 1 1 0 0 1 0 0 0 0 | 1 1 1 0 1 0 1 0 1 0 | 1 1 0 1 1 oo oo3oo3oo&#x | 1 1 | * * 48 * * | 0 0 0 1 1 1 1 0 0 0 | 0 0 0 1 1 1 1 1 1 0 | 0 1 1 1 1 .. .x .. .. | 0 2 | * * * 12 * | 0 0 0 0 2 0 0 1 1 0 | 0 0 0 1 0 0 2 2 0 1 | 0 1 1 0 2 .. .. .. .x | 0 2 | * * * * 12 | 0 0 0 0 0 0 2 0 1 1 | 0 0 0 0 0 1 0 2 2 1 | 0 0 1 1 2 ---------------+-------+---------------+--------------------------+-------------------------+---------- x. .. x. .. | 4 0 | 2 2 0 0 0 | 12 * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 0 1 0 .. o.3x. .. | 3 0 | 0 3 0 0 0 | * 8 * * * * * * * * | 1 0 1 0 0 0 1 0 0 0 | 1 1 0 0 1 .. .. x.3o. | 3 0 | 0 3 0 0 0 | * * 8 * * * * * * * | 0 1 1 0 0 0 0 0 1 0 | 1 0 0 1 1 xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 24 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 .. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * * 24 * * * * * | 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 1 .. .. xo ..&#x | 2 1 | 0 1 2 0 0 | * * * * * 24 * * * * | 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1 .. .. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * * * 24 * * * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1 .. .x3.o .. | 0 3 | 0 0 0 3 0 | * * * * * * * 4 * * | 0 0 0 0 0 0 2 0 0 1 | 0 1 0 0 2 .. .x .. .x | 0 4 | 0 0 0 2 2 | * * * * * * * * 6 * | 0 0 0 0 0 0 0 2 0 1 | 0 0 1 0 2 .. .. .o3.x | 0 3 | 0 0 0 0 3 | * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 2 1 | 0 0 0 1 2 ---------------+-------+---------------+--------------------------+-------------------------+---------- x. o.3x. .. ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * | 1 1 0 0 0 x. .. x.3o. ♦ 6 0 | 3 6 0 0 0 | 3 0 2 0 0 0 0 0 0 0 | * 4 * * * * * * * * | 1 0 0 1 0 .. o.3x.3o. ♦ 6 0 | 0 12 0 0 0 | 0 4 4 0 0 0 0 0 0 0 | * * 2 * * * * * * * | 1 0 0 0 1 xo ox .. ..&#x ♦ 2 2 | 1 0 4 1 0 | 1 0 0 2 2 0 0 0 0 0 | * * * 12 * * * * * * | 0 1 1 0 0 xo .. xo ..&#x ♦ 4 1 | 2 2 4 0 0 | 0 0 0 2 0 2 0 0 0 0 | * * * * 12 * * * * * | 0 1 0 1 0 xo .. .. ox&#x ♦ 2 2 | 1 0 4 0 1 | 0 0 0 2 0 0 2 0 0 0 | * * * * * 12 * * * * | 0 0 1 1 0 .. ox3xo ..&#x ♦ 3 3 | 0 3 6 3 0 | 0 1 0 0 3 3 0 1 0 0 | * * * * * * 8 * * * | 0 1 0 0 1 .. ox .. ox&#x ♦ 1 4 | 0 0 4 2 2 | 0 0 0 0 2 0 2 0 1 0 | * * * * * * * 12 * * | 0 0 1 0 1 .. .. xo3ox&#x ♦ 3 3 | 0 3 6 0 3 | 0 0 1 0 0 3 3 0 0 1 | * * * * * * * * 8 * | 0 0 0 1 1 .. .x3.o3.x ♦ 0 12 | 0 0 0 12 12 | 0 0 0 0 0 0 0 4 6 4 | * * * * * * * * * 1 | 0 0 0 0 2 ---------------+-------+---------------+--------------------------+-------------------------+---------- x. o.3x.3o. ♦ 12 0 | 6 24 0 0 0 | 12 8 8 0 0 0 0 0 0 0 | 4 4 2 0 0 0 0 0 0 0 | 1 * * * * xo ox3xo ..&#x ♦ 6 3 | 3 6 12 3 0 | 3 2 0 6 6 6 0 1 0 0 | 1 0 0 3 3 0 2 0 0 0 | * 4 * * * xo ox .. ox&#x ♦ 2 4 | 1 0 8 2 2 | 0 0 0 4 4 0 4 0 1 0 | 0 0 0 2 0 2 0 2 0 0 | * * 6 * * xo .. xo3ox&#x ♦ 6 3 | 3 6 12 0 3 | 3 0 2 6 0 6 6 0 0 1 | 0 1 0 0 3 3 0 0 2 0 | * * * 4 * .. ox3xo3ox&#x ♦ 6 12 | 0 12 24 12 12 | 0 4 4 0 12 12 12 4 6 4 | 0 0 1 0 0 0 4 6 4 1 | * * * * 2
oox3xxo3oox&#x → height(1,2) = 1 height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107 o..3o..3o.. | 6 * * | 4 1 4 0 0 0 0 | 2 2 4 4 2 4 2 0 0 0 0 0 0 0 0 | 1 2 2 2 4 2 2 1 2 0 0 0 0 0 | 1 2 1 2 1 0 .o.3.o.3.o. | * 6 * | 0 1 0 4 4 0 0 | 0 0 4 4 0 0 0 2 2 2 4 2 0 0 0 | 0 2 2 2 4 2 0 0 0 1 2 1 2 0 | 1 2 1 2 0 1 ..o3..o3..o | * * 12 | 0 0 2 0 2 2 2 | 0 0 0 2 2 1 2 0 0 2 1 2 1 2 1 | 0 0 0 2 1 2 1 2 1 0 1 2 1 1 | 0 1 2 1 1 1 ---------------+--------+---------------------+---------------------------------------+--------------------------------+------------ ... x.. ... | 2 0 0 | 12 * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0 oo.3oo.3oo.&#x | 1 1 0 | * 6 * * * * * ♦ 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 | 0 2 2 2 4 2 0 0 0 0 0 0 0 0 | 1 2 1 2 0 0 o.o3o.o3o.o&#x | 1 0 1 | * * 24 * * * * | 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0 ... .x. ... | 0 2 0 | * * * 12 * * * | 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 | 0 1 1 0 1 0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1 .oo3.oo3.oo&#x | 0 1 1 | * * * * 24 * * | 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 | 0 0 0 1 1 1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1 ..x ... ... | 0 0 2 | * * * * * 12 * | 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1 ... ... ..x | 0 0 2 | * * * * * * 12 | 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 | 0 0 0 0 0 1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1 ---------------+--------+---------------------+---------------------------------------+--------------------------------+------------ o..3x.. ... | 3 0 0 | 3 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * | 1 1 0 0 0 0 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0 ... x..3o.. | 3 0 0 | 3 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0 ... xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * * 12 * * * * * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 0 | * * * 24 * * * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 o.x ... ...&#x | 1 0 2 | 0 0 2 0 0 1 0 | * * * * 12 * * * * * * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0 ... x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 0 | * * * * * 12 * * * * * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0 ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * * * * 12 * * * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0 .o.3.x. ... | 0 3 0 | 0 0 0 3 0 0 0 | * * * * * * * 4 * * * * * * * | 0 1 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1 ... .x.3.o. | 0 3 0 | 0 0 0 3 0 0 0 | * * * * * * * * 4 * * * * * * | 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1 .ox ... ...&#x | 0 1 2 | 0 0 0 0 2 1 0 | * * * * * * * * * 12 * * * * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1 ... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 0 | * * * * * * * * * * 12 * * * * | 0 0 0 0 1 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1 ... ... .ox&#x | 0 1 2 | 0 0 0 0 2 0 1 | * * * * * * * * * * * 12 * * * | 0 0 0 0 0 1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1 ..x3..o ... | 0 0 3 | 0 0 0 0 0 3 0 | * * * * * * * * * * * * 4 * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1 ..x ... ..x | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * * * * * * 6 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1 ... ..o3..x | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1 ---------------+--------+---------------------+---------------------------------------+--------------------------------+------------ o..3x..3o.. ♦ 6 0 0 | 12 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 0 0 0 1 0 oo.3xx. ...&#x ♦ 3 3 0 | 3 3 0 3 0 0 0 | 1 0 3 0 0 0 0 1 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * | 1 1 0 0 0 0 ... xx.3oo.&#x ♦ 3 3 0 | 3 3 0 3 0 0 0 | 0 1 3 0 0 0 0 0 1 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * | 1 0 0 1 0 0 oox ... ...&#x ♦ 1 1 2 | 0 1 2 0 2 1 0 | 0 0 0 2 1 0 0 0 0 1 0 0 0 0 0 | * * * 12 * * * * * * * * * * | 0 1 1 0 0 0 ... xxo ...&#x ♦ 2 2 1 | 1 2 2 1 2 0 0 | 0 0 1 2 0 1 0 0 0 0 1 0 0 0 0 | * * * * 12 * * * * * * * * * | 0 1 0 1 0 0 ... ... oox&#x ♦ 1 1 2 | 0 1 2 0 2 0 1 | 0 0 0 2 0 0 1 0 0 0 0 1 0 0 0 | * * * * * 12 * * * * * * * * | 0 0 1 1 0 0 o.x3x.o ...&#x ♦ 3 0 3 | 3 0 6 0 0 3 0 | 1 0 0 0 3 3 0 0 0 0 0 0 1 0 0 | * * * * * * 4 * * * * * * * | 0 1 0 0 1 0 o.x ... o.x&#x ♦ 1 0 4 | 0 0 4 0 0 2 2 | 0 0 0 0 2 0 2 0 0 0 0 0 0 1 0 | * * * * * * * 6 * * * * * * | 0 0 1 0 1 0 ... x.o3o.x&#x ♦ 3 0 3 | 3 0 6 0 0 0 3 | 0 1 0 0 0 3 3 0 0 0 0 0 0 0 1 | * * * * * * * * 4 * * * * * | 0 0 0 1 1 0 .o.3.x.3.o. ♦ 0 6 0 | 0 0 0 12 0 0 0 | 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1 .ox3.xo ...&#x ♦ 0 3 3 | 0 0 0 3 6 3 0 | 0 0 0 0 0 0 0 1 0 3 3 0 1 0 0 | * * * * * * * * * * 4 * * * | 0 1 0 0 0 1 .ox ... .ox&#x ♦ 0 1 4 | 0 0 0 0 4 2 2 | 0 0 0 0 0 0 0 0 0 2 0 2 0 1 0 | * * * * * * * * * * * 6 * * | 0 0 1 0 0 1 ... .xo3.ox&#x ♦ 0 3 3 | 0 0 0 3 6 0 3 | 0 0 0 0 0 0 0 0 1 0 3 3 0 0 1 | * * * * * * * * * * * * 4 * | 0 0 0 1 0 1 ..x3..o3..x ♦ 0 0 12 | 0 0 0 0 0 12 12 | 0 0 0 0 0 0 0 0 0 0 0 0 4 6 4 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1 ---------------+--------+---------------------+---------------------------------------+--------------------------------+------------ oo.3xx.3oo.&#x ♦ 6 6 0 | 12 6 0 12 0 0 0 | 4 4 12 0 0 0 0 4 4 0 0 0 0 0 0 | 1 4 4 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * * oox3xxo ...&#x ♦ 3 3 3 | 3 3 6 3 6 3 0 | 1 0 3 6 3 3 0 1 0 3 3 0 1 0 0 | 0 1 0 3 3 0 1 0 0 0 1 0 0 0 | * 4 * * * * oox ... oox&#x ♦ 1 1 4 | 0 1 4 0 4 2 2 | 0 0 0 4 2 0 2 0 0 2 0 2 0 1 0 | 0 0 0 2 0 2 0 1 0 0 0 1 0 0 | * * 6 * * * ... xxo3oox&#x ♦ 3 3 3 | 3 3 6 3 6 0 3 | 0 1 3 6 0 3 3 0 1 0 3 3 0 0 1 | 0 0 1 0 3 3 0 0 1 0 0 0 1 0 | * * * 4 * * o.x3x.o3o.x&#x ♦ 6 0 12 | 12 0 24 0 0 12 12 | 4 4 0 0 12 12 12 0 0 0 0 0 4 6 4 | 1 0 0 0 0 0 4 6 4 0 0 0 0 1 | * * * * 1 * .ox3.xo3.ox&#x ♦ 0 6 12 | 0 0 0 12 24 12 12 | 0 0 0 0 0 0 0 4 4 12 12 12 4 6 4 | 0 0 0 0 0 0 0 0 0 1 4 6 4 1 | * * * * * 1
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