Acronym | hinsc |
Name |
demipenteractic scalene, demipenteractic-pyramid pyramid, line atop fully orthogonal demipenteract |
Circumradius | sqrt(3)/2 = 0.866025 |
Lace city in approx. ASCII-art |
o where: N o = o3o3o *b3o3o (pt) N = x3o3o *b3o3o (hin) o |
Face vector | 18, 113, 336, 520, 426, 173, 28 |
Confer |
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Incidence matrix according to Dynkin symbol
xo ox3oo3oo *c3oo3oo&#x → height = 1/sqrt(8) = 0.353553
(line || perp hin)
o. o.3o.3o. *c3o.3o. | 2 * ♦ 1 16 0 | 16 80 0 | 80 160 0 0 | 160 40 80 0 0 | 40 80 10 16 0 | 10 16 1
.o .o3.o3.o *c3.o3.o | * 16 ♦ 0 2 10 | 1 20 30 | 10 60 10 20 | 30 20 40 5 5 | 10 20 10 10 1 | 5 5 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
x. .. .. .. .. .. | 2 0 | 1 * * ♦ 16 0 0 | 80 0 0 0 | 160 0 0 0 0 | 40 80 0 0 0 | 10 16 0
oo oo3oo3oo *c3oo3oo&#x | 1 1 | * 32 * ♦ 1 10 0 | 10 30 0 0 | 30 10 20 0 0 | 10 20 5 5 0 | 5 5 1
.. .x .. .. .. .. | 0 2 | * * 80 ♦ 0 2 6 | 1 12 3 6 | 6 6 12 3 2 | 3 6 6 4 1 | 3 2 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | 16 * * ♦ 10 0 0 0 | 30 0 0 0 0 | 10 20 0 0 0 | 5 5 0
.. ox .. .. .. ..&#x | 1 2 | 0 2 1 | * 160 * ♦ 1 6 0 0 | 6 3 6 0 0 | 3 6 3 2 0 | 3 2 1
.. .x3.o .. .. .. | 0 3 | 0 0 3 | * * 160 | 0 2 1 2 | 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox .. .. .. ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 80 * * * ♦ 6 0 0 0 0 | 3 6 0 0 0 | 3 2 0
.. ox3oo .. .. ..&#x ♦ 1 3 | 0 3 3 | 0 3 1 | * 320 * * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1
.. .x3.o3.o .. .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * 40 * | 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2
.. .x3.o .. *c3.o .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * * 80 | 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox3oo .. .. ..&#x ♦ 2 3 | 1 6 3 | 3 6 1 | 3 2 0 0 | 160 * * * * | 1 2 0 0 0 | 2 1 0
.. ox3oo3oo .. ..&#x ♦ 1 4 | 0 4 6 | 0 6 4 | 0 4 1 0 | * 80 * * * | 1 0 2 0 0 | 2 0 1
.. ox3oo .. *c3oo ..&#x ♦ 1 4 | 0 4 6 | 0 6 4 | 0 4 0 1 | * * 160 * * | 0 1 1 1 0 | 1 1 1
.. .x3.o3.o *c3.o .. ♦ 0 8 | 0 0 24 | 0 0 32 | 0 0 8 8 | * * * 10 * | 0 0 2 0 1 | 1 0 2
.. .x3.o .. *c3.o3.o ♦ 0 5 | 0 0 10 | 0 0 10 | 0 0 0 5 | * * * * 16 | 0 0 0 2 1 | 0 1 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox3oo3oo .. ..&#x ♦ 2 4 | 1 8 6 | 4 12 4 | 6 8 1 0 | 4 2 0 0 0 | 40 * * * * | 2 0 0
xo ox3oo .. *c3oo ..&#x ♦ 2 4 | 1 8 6 | 4 12 4 | 6 8 0 1 | 4 0 2 0 0 | * 80 * * * | 1 1 0
.. ox3oo3oo *c3oo ..&#x ♦ 1 8 | 0 8 24 | 0 24 32 | 0 32 8 8 | 0 8 8 1 0 | * * 20 * * | 1 0 1
.. ox3oo .. *c3oo3oo&#x ♦ 1 5 | 0 5 10 | 0 10 10 | 0 10 0 5 | 0 0 5 0 1 | * * * 32 * | 0 1 1
.. .x3.o3.o *c3.o3.o ♦ 0 16 | 0 0 80 | 0 0 160 | 0 0 40 80 | 0 0 0 10 16 | * * * * 1 | 0 0 2
------------------------+------+---------+------------+--------------+------------------+---------------+--------
xo ox3oo3oo *c3oo ..&#x ♦ 2 8 | 1 16 24 | 8 48 32 | 24 64 8 8 | 32 16 16 1 0 | 8 8 2 0 0 | 10 * *
xo ox3oo .. *c3oo3oo&#x ♦ 2 5 | 1 10 10 | 5 20 10 | 10 20 0 5 | 10 0 10 0 1 | 0 5 0 2 0 | * 16 *
.. ox3oo3oo *c3oo3oo&#x ♦ 1 16 | 0 16 80 | 0 80 160 | 0 160 40 80 | 0 40 80 10 16 | 0 0 10 16 1 | * * 2
x(oo) o(xo) o(ox) o(xo)3o(oo)3o(ox)&#x → height(1,23) = 1/sqrt(8) = 0.353553 (line || tegum sum of 2 gyrated and lacings-orthogonal tepes) o(..) o(..) o(..) o(..)3o(..)3o(..) | 2 * ♦ 1 16 0 0 0 | 16 8 24 48 0 0 0 | 8 24 16 48 48 96 0 0 0 0 0 | 16 4 48 96 12 48 32 24 0 0 0 | 4 12 48 32 24 6 16 4 0 | 6 16 4 1 .(o.) .(o.) .(o.) .(o.)3.(o.)3.(o.) & | * 16 ♦ 0 2 1 3 6 | 1 2 6 12 3 9 18 | 1 3 6 6 18 36 1 3 12 8 6 | 3 2 9 18 6 24 16 12 3 5 2 | 1 3 12 8 6 6 10 4 1 | 3 5 2 2 -----------------------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+--------- x(..) .(..) .(..) .(..) .(..) .(..) | 2 0 | 1 * * * * ♦ 16 0 0 0 0 0 0 | 8 24 0 48 0 0 0 0 0 0 0 | 16 0 48 96 0 0 0 0 0 0 0 | 4 12 48 32 24 0 0 0 0 | 6 16 4 0 o(o.) o(o.) o(o.) o(o.)3o(o.)3o(o.)&#x & | 1 1 | * 32 * * * ♦ 1 1 3 6 0 0 0 | 1 3 3 6 9 18 0 0 0 0 0 | 3 1 9 18 3 12 8 6 0 0 0 | 1 3 12 8 6 3 5 2 0 | 3 5 2 1 .(..) .(x.) .(..) .(..) .(..) .(..) & | 0 2 | * * 8 * * ♦ 0 2 0 0 0 6 0 | 1 0 0 0 12 0 0 3 6 0 0 | 0 0 6 0 6 12 0 0 3 2 0 | 0 3 6 0 0 6 4 0 1 | 3 2 0 2 .(..) .(..) .(..) .(x.) .(..) .(..) & | 0 2 | * * * 24 * ♦ 0 0 2 0 2 0 4 | 0 1 4 0 0 8 1 0 2 4 2 | 2 2 0 4 0 4 8 4 1 2 2 | 1 0 2 4 2 2 4 4 1 | 1 2 2 2 .(oo) .(oo) .(oo) .(oo)3.(oo)3.(oo)&#x | 0 2 | * * * * 48 ♦ 0 0 0 2 0 2 4 | 0 0 0 1 4 8 0 1 4 2 2 | 0 0 2 4 2 8 4 4 2 2 1 | 0 1 4 2 2 4 4 2 1 | 2 2 1 2 -----------------------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+--------- x(o.) .(..) .(..) .(..) .(..) .(..)&#x & | 2 1 | 1 2 0 0 0 | 16 * * * * * * ♦ 1 3 0 6 0 0 0 0 0 0 0 | 3 0 9 18 0 0 0 0 0 0 0 | 1 3 12 8 6 0 0 0 0 | 3 5 2 0 .(..) o(x.) .(..) .(..) .(..) .(..)&#x & | 1 2 | 0 2 1 0 0 | * 16 * * * * * ♦ 1 0 0 0 6 0 0 0 0 0 0 | 0 0 6 0 3 6 0 0 0 0 0 | 0 3 6 0 0 3 2 0 0 | 3 2 0 1 .(..) .(..) .(..) o(x.) .(..) .(..)&#x & | 1 2 | 0 2 0 1 0 | * * 48 * * * * ♦ 0 1 2 0 0 4 0 0 0 0 0 | 2 1 0 4 0 2 4 2 0 0 0 | 1 0 2 4 2 1 2 2 0 | 1 2 2 1 o(oo) o(oo) o(oo) o(oo)3o(oo)3o(oo)&#x | 1 2 | 0 2 0 0 1 | * * * 96 * * * ♦ 0 0 0 1 2 4 0 0 0 0 0 | 0 0 2 4 1 4 2 2 0 0 0 | 0 1 4 2 2 2 2 1 0 | 2 2 1 1 .(..) .(..) .(..) .(x.)3.(o.) .(..) & | 0 3 | 0 0 0 3 0 | * * * * 16 * * | 0 0 2 0 0 0 1 0 0 2 0 | 1 2 0 0 0 0 4 0 0 1 2 | 1 0 0 2 0 0 2 4 1 | 0 1 2 2 .(..) .(xo) .(..) .(..) .(..) .(..)&#x & | 0 3 | 0 0 1 0 2 | * * * * * 48 * | 0 0 0 0 2 0 0 1 2 0 0 | 0 0 1 0 2 4 0 0 2 1 0 | 0 1 2 0 0 4 2 0 1 | 2 1 0 2 .(..) .(..) .(..) .(xo) .(..) .(..)&#x & | 0 3 | 0 0 0 1 2 | * * * * * * 96 | 0 0 0 0 0 2 0 0 1 1 1 | 0 0 0 1 0 2 2 2 1 1 1 | 0 0 1 1 1 2 2 2 1 | 1 1 1 2 -----------------------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+--------- x(o.) o(x.) .(..) .(..) .(..) .(..)&#x & ♦ 2 2 | 1 4 1 0 0 | 2 2 0 0 0 0 0 | 8 * * * * * * * * * * ♦ 0 0 6 0 0 0 0 0 0 0 0 | 0 3 6 0 0 0 0 0 0 | 3 2 0 0 x(o.) .(..) .(..) o(x.) .(..) .(..)&#x & ♦ 2 2 | 1 4 0 1 0 | 2 0 2 0 0 0 0 | * 24 * * * * * * * * * ♦ 2 0 0 4 0 0 0 0 0 0 0 | 1 0 2 4 2 0 0 0 0 | 1 2 2 0 .(..) .(..) .(..) o(x.)3o(o.) .(..)&#x & ♦ 1 3 | 0 3 0 3 0 | 0 0 3 0 1 0 0 | * * 32 * * * * * * * * | 1 1 0 0 0 0 2 0 0 0 0 | 1 0 0 2 0 0 1 2 0 | 0 1 2 1 x(oo) .(..) .(..) .(..) .(..) .(..)&#x & ♦ 2 2 | 1 4 0 0 1 | 2 0 0 2 0 0 0 | * * * 48 * * * * * * * ♦ 0 0 2 4 0 0 0 0 0 0 0 | 0 1 4 2 2 0 0 0 0 | 2 2 1 0 .(..) o(xo) .(..) .(..) .(..) .(..)&#x & ♦ 1 3 | 0 3 1 0 2 | 0 1 0 2 0 1 0 | * * * * 96 * * * * * * | 0 0 1 0 1 2 0 0 0 0 0 | 0 1 2 0 0 2 1 0 0 | 2 1 0 1 .(..) .(..) .(..) o(xo) .(..) .(..)&#x & ♦ 1 3 | 0 3 0 1 2 | 0 0 1 2 0 0 1 | * * * * * 192 * * * * * | 0 0 0 1 0 1 1 1 0 0 0 | 0 0 1 1 1 1 1 1 0 | 1 1 1 1 .(..) .(..) .(..) .(x.)3.(o.)3.(o.) & ♦ 0 4 | 0 0 0 6 0 | 0 0 0 0 4 0 0 | * * * * * * 4 * * * * | 0 2 0 0 0 0 0 0 0 0 2 | 1 0 0 0 0 0 0 4 1 | 0 0 2 2 .(..) .(xo) .(ox) .(..) .(..) .(..)&#x ♦ 0 4 | 0 0 2 0 4 | 0 0 0 0 0 4 0 | * * * * * * * 12 * * * | 0 0 0 0 2 0 0 0 2 0 0 | 0 1 0 0 0 4 0 0 1 | 2 0 0 2 .(..) .(xo) .(..) .(..) .(..) .(ox)&#x & ♦ 0 4 | 0 0 1 1 4 | 0 0 0 0 0 2 2 | * * * * * * * * 48 * * | 0 0 0 0 0 2 0 0 1 1 0 | 0 0 1 0 0 2 2 0 1 | 1 1 0 2 .(..) .(..) .(..) .(xo)3.(oo) .(..)&#x & ♦ 0 4 | 0 0 0 3 3 | 0 0 0 0 1 0 3 | * * * * * * * * * 32 * | 0 0 0 0 0 0 2 0 0 1 1 | 0 0 0 1 0 0 2 2 1 | 0 1 1 2 .(..) .(..) .(..) .(xo) .(..) .(ox)&#x ♦ 0 4 | 0 0 0 2 4 | 0 0 0 0 0 0 4 | * * * * * * * * * * 24 | 0 0 0 0 0 0 0 2 1 0 1 | 0 0 0 0 1 2 0 2 1 | 1 0 1 2 -----------------------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+--------- x(o.) .(..) .(..) o(x.)3o(o.) .(..)&#x & ♦ 2 3 | 1 6 0 3 0 | 3 0 6 0 1 0 0 | 0 3 2 0 0 0 0 0 0 0 0 | 16 * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 | 0 1 2 0 .(..) .(..) .(..) o(x.)3o(o.)3o(o.)&#x & ♦ 1 4 | 0 4 0 6 0 | 0 0 6 0 4 0 0 | 0 0 4 0 0 0 1 0 0 0 0 | * 8 * * * * * * * * * | 1 0 0 0 0 0 0 2 0 | 0 0 2 1 x(oo) o(xo) .(..) .(..) .(..) .(..)&#x & ♦ 2 3 | 1 6 1 0 2 | 3 2 0 4 0 1 0 | 1 0 0 2 2 0 0 0 0 0 0 | * * 48 * * * * * * * * | 0 1 2 0 0 0 0 0 0 | 2 1 0 0 x(oo) .(..) .(..) o(xo) .(..) .(..)&#x & ♦ 2 3 | 1 6 0 1 2 | 3 0 2 4 0 0 1 | 0 1 0 2 0 2 0 0 0 0 0 | * * * 96 * * * * * * * | 0 0 1 1 1 0 0 0 0 | 1 1 1 0 .(..) o(xo) o(ox) .(..) .(..) .(..)&#x ♦ 1 4 | 0 4 2 0 4 | 0 2 0 4 0 4 0 | 0 0 0 0 4 0 0 1 0 0 0 | * * * * 24 * * * * * * | 0 1 0 0 0 2 0 0 0 | 2 0 0 1 .(..) o(xo) .(..) .(..) .(..) o(ox)&#x & ♦ 1 4 | 0 4 1 1 4 | 0 1 1 4 0 2 2 | 0 0 0 0 2 2 0 0 1 0 0 | * * * * * 96 * * * * * | 0 0 1 0 0 1 1 0 0 | 1 1 0 1 .(..) .(..) .(..) o(xo)3o(oo) .(..)&#x & ♦ 1 4 | 0 4 0 3 3 | 0 0 3 3 1 0 3 | 0 0 1 0 0 3 0 0 0 1 0 | * * * * * * 64 * * * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 1 .(..) .(..) .(..) o(xo) .(..) o(ox)&#x ♦ 1 4 | 0 4 0 2 4 | 0 0 2 4 0 0 4 | 0 0 0 0 0 4 0 0 0 0 1 | * * * * * * * 48 * * * | 0 0 0 0 1 1 0 1 0 | 1 0 1 1 .(..) .(xo) .(ox) .(xo) .(..) .(ox)&#zx ♦ 0 8 | 0 0 4 4 16 | 0 0 0 0 0 16 16 | 0 0 0 0 0 0 0 4 8 0 4 | * * * * * * * * 6 * * | 0 0 0 0 0 2 0 0 1 | 1 0 0 2 .(..) .(xo) .(..) .(..) .(oo)3.(ox)&#x & ♦ 0 5 | 0 0 1 3 6 | 0 0 0 0 1 3 6 | 0 0 0 0 0 0 0 0 3 2 0 | * * * * * * * * * 16 * | 0 0 0 0 0 0 2 0 1 | 0 1 0 2 .(..) .(..) .(..) .(xo)3.(oo)3.(ox)&#x ♦ 0 8 | 0 0 0 12 12 | 0 0 0 0 8 0 24 | 0 0 0 0 0 0 2 0 0 8 6 | * * * * * * * * * * 4 | 0 0 0 0 0 0 0 2 1 | 0 0 1 2 -----------------------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+--------- x(o.) .(..) .(..) o(x.)3o(o.)3o(o.)&#x & ♦ 2 4 | 1 8 0 6 0 | 4 0 12 0 4 0 0 | 0 6 8 0 0 0 1 0 0 0 0 | 4 2 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * | 0 0 2 0 x(oo) o(xo) o(ox) .(..) .(..) .(..)&#x ♦ 2 4 | 1 8 2 0 4 | 4 4 0 8 0 4 0 | 2 0 0 4 8 0 0 1 0 0 0 | 0 0 4 0 2 0 0 0 0 0 0 | * 12 * * * * * * * | 2 0 0 0 x(oo) o(xo) .(..) .(..) .(..) o(ox)&#x & ♦ 2 4 | 1 8 1 1 4 | 4 2 2 8 0 2 2 | 1 1 0 4 4 4 0 0 1 0 0 | 0 0 2 2 0 2 0 0 0 0 0 | * * 48 * * * * * * | 1 1 0 0 x(oo) .(..) .(..) o(xo)3o(oo) .(..)&#x & ♦ 2 4 | 1 8 0 3 3 | 4 0 6 6 1 0 3 | 0 3 2 3 0 6 0 0 0 1 0 | 1 0 0 3 0 0 2 0 0 0 0 | * * * 32 * * * * * | 0 1 1 0 x(oo) .(..) .(..) o(xo) .(..) o(ox)&#x ♦ 2 4 | 1 8 0 2 4 | 4 0 4 8 0 0 4 | 0 2 0 4 0 8 0 0 0 0 1 | 0 0 0 4 0 0 0 2 0 0 0 | * * * * 24 * * * * | 1 0 1 0 .(..) o(xo) o(ox) o(xo) .(..) o(ox)&#x ♦ 1 8 | 0 8 4 4 16 | 0 4 4 16 0 16 16 | 0 0 0 0 16 16 0 4 8 0 4 | 0 0 0 0 4 8 0 4 1 0 0 | * * * * * 12 * * * | 1 0 0 1 .(..) o(xo) .(..) .(..) o(oo)3o(ox)&#x & ♦ 1 5 | 0 5 1 3 6 | 0 1 3 6 1 3 6 | 0 0 1 0 3 6 0 0 3 2 0 | 0 0 0 0 0 3 2 0 0 1 0 | * * * * * * 32 * * | 0 1 0 1 .(..) .(..) .(..) o(xo)3o(oo)3o(ox)&#x ♦ 1 8 | 0 8 0 12 12 | 0 0 12 12 8 0 24 | 0 0 8 0 0 24 2 0 0 8 6 | 0 2 0 0 0 0 8 6 0 0 1 | * * * * * * * 8 * | 0 0 1 1 .(..) .(xo) .(ox) .(xo)3.(oo)3.(ox)&#zx ♦ 0 16 | 0 0 8 24 48 | 0 0 0 0 16 48 96 | 0 0 0 0 0 0 4 12 48 32 24 | 0 0 0 0 0 0 0 0 6 16 4 | * * * * * * * * 1 | 0 0 0 2 -----------------------------------------+------+--------------+----------------------+---------------------------------+-------------------------------+-------------------------+--------- x(oo) o(xo) o(ox) o(xo) .(..) o(ox)&#x ♦ 2 8 | 1 16 4 4 16 | 8 8 8 32 0 16 16 | 4 4 0 16 32 32 0 4 8 0 4 | 0 0 16 16 8 16 0 8 1 0 0 | 0 4 8 0 4 2 0 0 0 | 6 * * * x(oo) o(xo) .(..) .(..) o(oo)3o(ox)&#x & ♦ 2 5 | 1 10 1 3 6 | 5 2 6 12 1 3 6 | 1 3 2 6 6 12 0 0 3 2 0 | 1 0 3 6 0 6 4 0 0 1 0 | 0 0 3 2 0 0 2 0 0 | * 16 * * x(oo) .(..) .(..) o(xo)3o(oo)3o(ox)&#x ♦ 2 8 | 1 16 0 12 12 | 8 0 24 24 8 0 24 | 0 12 16 12 0 48 2 0 0 8 6 | 8 4 0 24 0 0 16 12 0 0 1 | 2 0 0 8 6 0 0 2 0 | * * 4 * .(..) o(xo) o(ox) o(xo)3o(oo)3o(ox)&#x ♦ 1 16 | 0 16 8 24 48 | 0 8 24 48 16 48 96 | 0 0 16 0 48 96 4 12 48 32 24 | 0 4 0 0 12 48 32 24 6 16 4 | 0 0 0 0 0 6 16 4 1 | * * * 2
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