Acronym | dihin (alt.: penalrap) | ||
Name |
(vertex-)diminished hemipenteract, pentachoron atop alternate rectified pentachoron | ||
Circumradius | sqrt(5/8) = 0.790569 | ||
Lace city in approx. ASCII-art |
+----- oo3ox3oo&#x (octpy) / +-- xo3oo3ox&#x (alt. hex) / / O t -- o3o3x3o (rap) o T -- x3o3o3o (inv pen) \ +-- o3x3o3o (inv rap) where: o = o3o3o (point) T = x3o3o (tet) O = o3x3o (oct) t = o3o3x (dual tet) | ||
Lace hyper city in approx. ASCII-art |
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Face vector | 15, 70, 130, 95, 22 | ||
Confer |
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External links |
Incidence matrix according to Dynkin symbol
oo3xo3oo3ox&#x → height = sqrt(2/5) = 0.632456
(rap || inv pen)
o.3o.3o.3o. | 10 * ♦ 6 3 0 | 3 6 12 3 0 | 3 2 6 6 6 1 0 | 1 3 3 2 0
.o3.o3.o3.o | * 5 ♦ 0 6 4 | 0 0 12 12 6 | 0 0 4 4 12 6 4 | 0 1 4 4 1
---------------+------+----------+----------------+-------------------+-----------
.. x. .. .. | 2 0 | 30 * * | 1 2 2 0 0 | 2 1 2 2 1 0 0 | 1 2 1 1 0
oo3oo3oo3oo&#x | 1 1 | * 30 * ♦ 0 0 4 2 0 | 0 0 2 2 4 1 0 | 0 1 2 2 0
.. .. .. .x | 0 2 | * * 10 ♦ 0 0 0 3 3 | 0 0 0 0 3 3 3 | 0 0 1 3 1
---------------+------+----------+----------------+-------------------+-----------
o.3x. .. .. | 3 0 | 3 0 0 | 10 * * * * | 2 2 0 0 0 0 0 | 1 2 1 0 0
.. x.3o. .. | 3 0 | 3 0 0 | * 20 * * * | 1 1 0 1 0 0 0 | 1 1 0 1 0
.. xo .. ..&#x | 2 1 | 1 2 0 | * * 60 * * | 0 0 1 1 1 0 0 | 0 1 1 1 0
.. .. .. ox&#x | 1 2 | 0 2 1 | * * * 30 * | 0 0 0 0 2 1 0 | 0 0 1 2 0
.. .. .o3.x | 0 3 | 0 0 3 | * * * * 10 | 0 0 0 0 0 1 2 | 0 0 0 2 1
---------------+------+----------+----------------+-------------------+-----------
o.3x.3o. ..&#x ♦ 6 0 | 12 0 0 | 4 4 0 0 0 | 5 * * * * * * | 1 1 0 0 0
.. x.3o.3o. ♦ 4 0 | 6 0 0 | 0 4 0 0 0 | * 5 * * * * * | 1 0 0 1 0
oo3xo .. ..&#x ♦ 3 1 | 3 3 0 | 1 0 3 0 0 | * * 20 * * * * | 0 1 1 0 0
.. xo3oo ..&#x ♦ 3 1 | 3 3 0 | 0 1 3 0 0 | * * * 20 * * * | 0 1 0 1 0
.. xo .. ox&#x ♦ 2 2 | 1 4 1 | 0 0 2 2 0 | * * * * 30 * * | 0 0 1 1 0
.. .. oo3ox&#x ♦ 1 3 | 0 3 3 | 0 0 0 3 1 | * * * * * 10 * | 0 0 0 2 0
.. .o3.o3.x ♦ 0 4 | 0 0 6 | 0 0 0 0 4 | * * * * * * 5 | 0 0 0 1 1
---------------+------+----------+----------------+-------------------+-----------
o.3x.3o.3o.&#x ♦ 10 0 | 30 0 0 | 10 20 0 0 0 | 5 5 0 0 0 0 0 | 1 * * * *
oo3xo3oo ..&#x ♦ 6 1 | 12 6 0 | 4 4 12 0 0 | 1 0 4 4 0 0 0 | * 5 * * *
oo3xo .. ox&#x ♦ 3 2 | 3 6 1 | 1 0 6 3 0 | 0 0 2 0 3 0 0 | * * 10 * *
.. xo3oo3ox&#x ♦ 4 4 | 6 12 6 | 0 4 12 12 4 | 0 1 0 4 6 4 1 | * * * 5 *
.o3.o3.o3.x ♦ 0 5 | 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * 1
ooxo3oxoo3ooox&#xr → height(1,2) = height(3,4) = 1/sqrt(2) = 0.707107 height(1,4) = height(2,3) = height(2,4) sqrt(5/8) = 0.790569 o...3o...3o... | 1 * * * ♦ 6 4 0 0 0 0 0 0 | 12 6 12 0 0 0 0 0 0 0 0 0 0 0 | 4 4 4 12 6 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 4 4 0 0 0 0 .o..3.o..3.o.. | * 6 * * ♦ 1 0 4 2 2 0 0 0 | 4 0 2 2 2 1 4 4 1 4 0 0 0 0 | 2 2 0 4 1 1 2 2 2 2 4 2 0 0 0 0 0 | 1 0 2 2 1 2 1 0 ..o.3..o.3..o. | * * 4 * ♦ 0 0 0 3 0 3 3 0 | 0 0 0 0 0 3 3 0 0 6 3 6 3 0 | 0 0 0 0 0 0 3 1 0 6 3 3 1 3 3 1 0 | 0 0 0 1 1 3 3 1 ...o3...o3...o | * * * 4 ♦ 0 1 0 0 3 0 3 3 | 0 3 3 0 0 0 0 3 3 6 0 3 6 3 | 0 0 3 3 3 0 0 0 1 3 3 6 0 1 3 3 1 | 0 1 1 3 0 1 3 1 -------------------+---------+---------------------+------------------------------------+---------------------------------------+---------------- oo..3oo..3oo..&#x | 1 1 0 0 | 6 * * * * * * * ♦ 4 0 2 0 0 0 0 0 0 0 0 0 0 0 | 2 2 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 2 2 0 0 0 0 o..o3o..o3o..o&#x | 1 0 0 1 | * 4 * * * * * * ♦ 0 3 3 0 0 0 0 0 0 0 0 0 0 0 | 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 3 0 0 0 0 .... .x.. .... | 0 2 0 0 | * * 12 * * * * * | 1 0 0 1 1 0 1 1 0 0 0 0 0 0 | 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 | 1 0 1 1 1 1 0 0 .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * 12 * * * * | 0 0 0 0 0 1 2 0 0 2 0 0 0 0 | 0 0 0 0 0 0 2 1 0 2 2 1 0 0 0 0 0 | 0 0 0 1 1 2 1 0 .o.o3.o.o3.o.o&#x | 0 1 0 1 | * * * * 12 * * * ♦ 0 0 1 0 0 0 0 2 1 2 0 0 0 0 | 0 0 0 2 1 0 0 0 1 1 2 2 0 0 0 0 0 | 0 0 1 2 0 1 1 0 ..x. .... .... | 0 0 2 0 | * * * * * 6 * * | 0 0 0 0 0 1 0 0 0 0 2 2 0 0 | 0 0 0 0 0 0 2 0 0 2 0 0 1 2 1 0 0 | 0 0 0 0 1 2 1 1 ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * 12 * ♦ 0 0 0 0 0 0 0 0 0 2 0 2 2 0 | 0 0 0 0 0 0 0 0 0 2 1 2 0 1 2 1 0 | 0 0 0 1 0 1 2 1 .... .... ...x | 0 0 0 2 | * * * * * * * 6 ♦ 0 1 0 0 0 0 0 0 1 0 0 0 2 2 | 0 0 2 0 1 0 0 0 0 0 0 2 0 0 1 2 1 | 0 1 0 2 0 0 1 1 -------------------+---------+---------------------+------------------------------------+---------------------------------------+---------------- .... ox.. ....&#x | 1 2 0 0 | 2 0 1 0 0 0 0 0 | 12 * * * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 0 .... .... o..x&#x | 1 0 0 2 | 0 2 0 0 0 0 0 1 | * 6 * * * * * * * * * * * * | 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 2 0 0 0 0 oo.o3oo.o3oo.o&#x | 1 1 0 1 | 1 1 0 0 1 0 0 0 | * * 12 * * * * * * * * * * * | 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 2 0 0 0 0 .o..3.x.. .... | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * * 4 * * * * * * * * * * | 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 | 1 0 1 0 1 1 0 0 .... .x..3.o.. | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * * * 4 * * * * * * * * * | 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 0 0 1 1 0 0 0 .ox. .... ....&#x | 0 1 2 0 | 0 0 0 2 0 1 0 0 | * * * * * 6 * * * * * * * * | 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 | 0 0 0 0 1 2 1 0 .... .xo. ....&#x | 0 2 1 0 | 0 0 1 2 0 0 0 0 | * * * * * * 12 * * * * * * * | 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 | 0 0 0 1 1 1 0 0 .... .x.o ....&#x | 0 2 0 1 | 0 0 1 0 2 0 0 0 | * * * * * * * 12 * * * * * * | 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 | 0 0 1 1 0 1 0 0 .... .... .o.x&#x | 0 1 0 2 | 0 0 0 0 2 0 0 1 | * * * * * * * * 6 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 | 0 0 0 2 0 0 1 0 .ooo3.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 1 1 0 1 0 | * * * * * * * * * 24 * * * * | 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 0 1 0 1 1 0 ..x.3..o. .... | 0 0 3 0 | 0 0 0 0 0 3 0 0 | * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 | 0 0 0 0 1 1 0 1 ..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * * * * 12 * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 | 0 0 0 0 0 1 1 1 .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * 12 * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 0 0 1 1 .... ...o3...x | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * 4 | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 | 0 1 0 1 0 0 0 1 -------------------+---------+---------------------+------------------------------------+---------------------------------------+---------------- oo..3ox.. ....&#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 0 0 | 4 * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 .... ox..3oo..&#x ♦ 1 3 0 0 | 3 0 3 0 0 0 0 0 | 3 0 0 0 1 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 .... o..o3o..x&#x ♦ 1 0 0 3 | 0 3 0 0 0 0 0 3 | 0 3 0 0 0 0 0 0 0 0 0 0 0 1 | * * 4 * * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 .... ox.o ....&#x ♦ 1 2 0 1 | 2 1 1 0 2 0 0 0 | 1 0 2 0 0 0 0 1 0 0 0 0 0 0 | * * * 12 * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 .... .... oo.x&#x ♦ 1 1 0 2 | 1 2 0 0 2 0 0 1 | 0 1 2 0 0 0 0 0 1 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * | 0 0 0 2 0 0 0 0 .o..3.x..3.o.. ♦ 0 6 0 0 | 0 0 12 0 0 0 0 0 | 0 0 0 4 4 0 0 0 0 0 0 0 0 0 | * * * * * 1 * * * * * * * * * * * | 1 0 0 0 1 0 0 0 .ox.3.xo. ....&#x ♦ 0 3 3 0 | 0 0 3 6 0 3 0 0 | 0 0 0 1 0 3 3 0 0 0 1 0 0 0 | * * * * * * 4 * * * * * * * * * * | 0 0 0 0 1 1 0 0 .... .xo.3.oo.&#x ♦ 0 3 1 0 | 0 0 3 3 0 0 0 0 | 0 0 0 0 1 0 3 0 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * * * | 0 0 0 1 1 0 0 0 .o.o3.x.o ....&#x ♦ 0 3 0 1 | 0 0 3 0 3 0 0 0 | 0 0 0 1 0 0 0 3 0 0 0 0 0 0 | * * * * * * * * 4 * * * * * * * * | 0 0 1 0 0 1 0 0 .oxo .... ....&#x ♦ 0 1 2 1 | 0 0 0 2 1 1 2 0 | 0 0 0 0 0 1 0 0 0 2 0 1 0 0 | * * * * * * * * * 12 * * * * * * * | 0 0 0 0 0 1 1 0 .... .xoo ....&#x ♦ 0 2 1 1 | 0 0 1 2 2 0 1 0 | 0 0 0 0 0 0 1 1 0 2 0 0 0 0 | * * * * * * * * * * 12 * * * * * * | 0 0 0 1 0 1 0 0 .... .... .oox&#x ♦ 0 1 1 2 | 0 0 0 1 2 0 2 1 | 0 0 0 0 0 0 0 0 1 2 0 0 1 0 | * * * * * * * * * * * 12 * * * * * | 0 0 0 1 0 0 1 0 ..x.3..o.3..o. ♦ 0 0 4 0 | 0 0 0 0 0 6 0 0 | 0 0 0 0 0 0 0 0 0 0 4 0 0 0 | * * * * * * * * * * * * 1 * * * * | 0 0 0 0 1 0 0 1 ..xo3..oo ....&#x ♦ 0 0 3 1 | 0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 0 0 0 0 1 3 0 0 | * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 1 0 1 ..xo .... ..ox&#x ♦ 0 0 2 2 | 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * * * 6 * * | 0 0 0 0 0 0 1 1 .... ..oo3..ox&#x ♦ 0 0 1 3 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * * * * * * 4 * | 0 0 0 1 0 0 0 1 ...o3...o3...x ♦ 0 0 0 4 | 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * * 1 | 0 1 0 0 0 0 0 1 -------------------+---------+---------------------+------------------------------------+---------------------------------------+---------------- oo..3ox..3oo..&#x ♦ 1 6 0 0 | 6 0 12 0 0 0 0 0 | 12 0 0 4 4 0 0 0 0 0 0 0 0 0 | 4 4 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * o..o3o..o3o..x&#x ♦ 1 0 0 4 | 0 4 0 0 0 0 0 6 | 0 6 0 0 0 0 0 0 0 0 0 0 0 4 | 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | * 1 * * * * * * oo.o3ox.o ....&#x ♦ 1 3 0 1 | 3 1 3 0 3 0 0 0 | 3 0 3 1 0 0 0 3 0 0 0 0 0 0 | 1 0 0 3 0 0 0 0 1 0 0 0 0 0 0 0 0 | * * 4 * * * * * .... oxoo3ooox&#xr ♦ 1 3 1 3 | 3 3 3 3 6 0 3 3 | 3 3 6 0 1 0 3 3 3 6 0 0 3 1 | 0 1 1 3 3 0 0 1 0 0 3 3 0 0 0 1 0 | * * * 4 * * * * .ox.3.xo.3.oo.&#x ♦ 0 6 4 0 | 0 0 12 12 0 6 0 0 | 0 0 0 4 4 6 12 0 0 0 4 0 0 0 | 0 0 0 0 0 1 4 4 0 0 0 0 1 0 0 0 0 | * * * * 1 * * * .oxo3.xoo ....&#x ♦ 0 3 3 1 | 0 0 3 6 3 3 3 0 | 0 0 0 1 0 3 3 3 0 6 1 3 0 0 | 0 0 0 0 0 0 1 0 1 3 3 0 0 1 0 0 0 | * * * * * 4 * * .oxo .... .oox&#x ♦ 0 1 2 2 | 0 0 0 2 2 1 4 1 | 0 0 0 0 0 1 0 0 1 4 0 2 2 0 | 0 0 0 0 0 0 0 0 0 2 0 2 0 0 1 0 0 | * * * * * * 6 * ..xo3..oo3..ox&#x ♦ 0 0 4 4 | 0 0 0 0 0 6 12 6 | 0 0 0 0 0 0 0 0 0 0 4 12 12 4 | 0 0 0 0 0 0 0 0 0 0 0 0 1 4 6 4 1 | * * * * * * * 1
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