Acronym | squix |
Name |
square hixene, square atop fully orthogonal pentachoron |
|,>,O device | line prism pyramid pyramid pyramid pyramid pyramid = ||>>>>> |
Circumradius | 1/sqrt(2) = 0.707107 |
Face vector | 9, 34, 71, 90, 71, 34, 9 |
Confer |
|
Incidence matrix according to Dynkin symbol
xo4oo ox3oo3oo3oo&#x → height = 1/sqrt(10) = 0.316228
({4} || perp pen)
o.4o. o.3o.3o.3o. | 4 * | 2 5 0 | 1 10 10 0 | 5 20 10 0 | 10 20 5 0 | 10 10 1 | 5 2
.o4.o .o3.o3.o3.o | * 5 ♦ 0 4 4 | 0 4 16 6 | 1 16 24 4 | 4 24 16 1 | 6 16 4 | 4 4
---------------------+-----+---------+------------+-----------+------------+---------+----
x. .. .. .. .. .. | 2 0 | 4 * * | 1 5 0 0 | 5 10 0 0 | 10 10 0 0 | 10 5 0 | 5 1
oo4oo oo3oo3oo3oo&#x | 1 1 | * 20 * | 0 2 4 0 | 1 8 6 0 | 4 12 4 0 | 6 8 1 | 4 2
.. .. .x .. .. .. | 0 2 | * * 10 ♦ 0 0 4 3 | 0 4 12 3 | 1 12 12 1 | 3 12 4 | 3 4
---------------------+-----+---------+------------+-----------+------------+---------+----
x.4o. .. .. .. .. | 4 0 | 4 0 0 | 1 * * * ♦ 5 0 0 0 | 10 0 0 0 | 10 0 0 | 5 0
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 20 * * | 1 4 0 0 | 4 6 0 0 | 6 4 0 | 4 1
.. .. ox .. .. ..&#x | 1 2 | 0 2 1 | * * 40 * | 0 2 3 0 | 1 6 3 0 | 3 6 1 | 3 2
.. .. .x3.o .. .. | 0 3 | 0 0 3 | * * * 10 ♦ 0 0 4 2 | 0 4 8 1 | 1 8 4 | 2 4
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo .. .. .. ..&#x ♦ 4 1 | 4 4 0 | 1 4 0 0 | 5 * * * ♦ 4 0 0 0 | 6 0 0 | 4 0
xo .. ox .. .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * 40 * * | 1 3 0 0 | 3 3 0 | 3 1
.. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * 40 * | 0 2 2 0 | 1 4 1 | 2 2
.. .. .x3.o3.o .. ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * 5 ♦ 0 0 4 1 | 0 4 4 | 1 4
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo ox .. .. ..&#x ♦ 4 2 | 4 8 1 | 1 8 4 0 | 2 4 0 0 | 10 * * * | 3 0 0 | 3 0
xo .. ox3oo .. ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 3 2 0 | * 40 * * | 1 2 0 | 2 1
.. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 4 1 | * * 20 * | 0 2 1 | 1 2
.. .. .x3.o3.o3.o ♦ 0 5 | 0 0 10 | 0 0 0 10 | 0 0 0 5 | * * * 1 | 0 0 4 | 0 4
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo ox3oo .. ..&#x ♦ 4 3 | 4 12 3 | 1 12 12 1 | 3 12 4 0 | 3 4 0 0 | 10 * * | 2 0
xo .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 6 | 0 4 12 4 | 0 6 8 1 | 0 4 2 0 | * 20 * | 1 1
.. .. ox3oo3oo3oo&#x ♦ 1 5 | 0 5 10 | 0 0 10 10 | 0 0 10 5 | 0 0 5 1 | * * 4 | 0 2
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo ox3oo3oo ..&#x ♦ 4 4 | 4 16 6 | 1 16 24 4 | 4 24 16 1 | 6 16 4 0 | 4 4 0 | 5 *
xo .. ox3oo3oo3oo&#x ♦ 2 5 | 1 10 10 | 0 5 20 10 | 0 10 20 5 | 0 10 10 1 | 0 5 2 | * 4
xo xo ox3oo3oo3oo&#x → height = 1/sqrt(10) = 0.316228
({4} || perp pen)
o. o. o.3o.3o.3o. | 4 * | 1 1 5 0 | 1 5 5 10 0 | 5 10 10 10 0 | 10 10 10 5 0 | 10 5 5 1 | 5 1 1
.o .o .o3.o3.o3.o | * 5 ♦ 0 0 4 4 | 0 2 2 16 6 | 1 8 8 24 4 | 4 12 12 16 1 | 6 8 8 4 | 4 2 2
---------------------+-----+-----------+---------------+--------------+---------------+------------+------
x. .. .. .. .. .. | 2 0 | 2 * * * | 1 5 0 0 0 | 5 10 0 0 0 | 10 10 0 0 0 | 10 5 0 0 | 5 1 0
.. x. .. .. .. .. | 2 0 | * 2 * * | 1 0 5 0 0 | 5 0 10 0 0 | 10 0 10 0 0 | 10 0 5 0 | 5 0 1
oo oo oo3oo3oo3oo&#x | 1 1 | * * 20 * | 0 1 1 4 0 | 1 4 4 6 0 | 4 6 6 4 0 | 6 4 4 1 | 4 1 1
.. .. .x .. .. .. | 0 2 | * * * 10 ♦ 0 0 0 4 3 | 0 2 2 12 3 | 1 6 6 12 1 | 3 6 6 4 | 3 2 2
---------------------+-----+-----------+---------------+--------------+---------------+------------+------
x. x. .. .. .. .. | 4 0 | 2 2 0 0 | 1 * * * * ♦ 5 0 0 0 0 | 10 0 0 0 0 | 10 0 0 0 | 5 0 0
xo .. .. .. .. ..&#x | 2 1 | 1 0 2 0 | * 10 * * * | 1 4 0 0 0 | 4 6 0 0 0 | 6 4 0 0 | 4 1 0
.. xo .. .. .. ..&#x | 2 1 | 0 1 2 0 | * * 10 * * | 1 0 4 0 0 | 4 0 6 0 0 | 6 0 4 0 | 4 0 1
.. .. ox .. .. ..&#x | 1 2 | 0 0 2 1 | * * * 40 * | 0 1 1 3 0 | 1 3 3 3 0 | 3 3 3 1 | 3 1 1
.. .. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * * 10 ♦ 0 0 0 4 2 | 0 2 2 8 1 | 1 4 4 4 | 2 2 2
---------------------+-----+-----------+---------------+--------------+---------------+------------+------
xo xo .. .. .. ..&#x ♦ 4 1 | 2 2 4 0 | 1 2 2 0 0 | 5 * * * * ♦ 4 0 0 0 0 | 6 0 0 0 | 4 0 0
xo .. ox .. .. ..&#x ♦ 2 2 | 1 0 4 1 | 0 2 0 2 0 | * 20 * * * | 1 3 0 0 0 | 3 3 0 0 | 3 1 0
.. xo ox .. .. ..&#x ♦ 2 2 | 0 1 4 1 | 0 0 2 2 0 | * * 20 * * | 1 0 3 0 0 | 3 0 3 0 | 3 0 1
.. .. ox3oo .. ..&#x ♦ 1 3 | 0 0 3 3 | 0 0 0 3 1 | * * * 40 * | 0 1 1 2 0 | 1 2 2 1 | 2 1 1
.. .. .x3.o3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * 5 ♦ 0 0 0 4 1 | 0 2 2 4 | 1 2 2
---------------------+-----+-----------+---------------+--------------+---------------+------------+------
xo xo ox .. .. ..&#x ♦ 4 2 | 2 2 8 1 | 1 4 4 4 0 | 2 2 2 0 0 | 10 * * * * | 3 0 0 0 | 3 0 0
xo .. ox3oo .. ..&#x ♦ 2 3 | 1 0 6 3 | 0 3 0 6 1 | 0 3 0 2 0 | * 20 * * * | 1 2 0 0 | 2 1 0
.. xo ox3oo .. ..&#x ♦ 2 3 | 0 1 6 3 | 0 0 3 6 1 | 0 0 3 2 0 | * * 20 * * | 1 0 2 0 | 2 0 1
.. .. ox3oo3oo ..&#x ♦ 1 4 | 0 0 4 6 | 0 0 0 6 4 | 0 0 0 4 1 | * * * 20 * | 0 1 1 1 | 1 1 1
.. .. .x3.o3.o3.o ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 5 | * * * * 1 | 0 0 0 4 | 0 2 2
---------------------+-----+-----------+---------------+--------------+---------------+------------+------
xo xo ox3oo .. ..&#x ♦ 4 3 | 2 2 12 3 | 1 6 6 12 1 | 3 6 6 4 0 | 3 2 2 0 0 | 10 * * * | 2 0 0
xo .. ox3oo3oo ..&#x ♦ 2 4 | 1 0 8 6 | 0 4 0 12 4 | 0 6 0 8 1 | 0 4 0 2 0 | * 10 * * | 1 1 0
.. xo ox3oo3oo ..&#x ♦ 2 4 | 0 1 8 6 | 0 0 4 12 4 | 0 0 6 8 1 | 0 0 4 2 0 | * * 10 * | 1 0 1
.. .. ox3oo3oo3oo&#x ♦ 1 5 | 0 0 5 10 | 0 0 0 10 10 | 0 0 0 10 5 | 0 0 0 5 1 | * * * 4 | 0 1 1
---------------------+-----+-----------+---------------+--------------+---------------+------------+------
xo xo ox3oo3oo ..&#x ♦ 4 4 | 2 2 16 6 | 1 8 8 24 4 | 4 12 12 16 1 | 6 8 8 4 0 | 4 2 2 0 | 5 * *
xo .. ox3oo3oo3oo&#x ♦ 2 5 | 1 0 10 10 | 0 5 0 20 10 | 0 10 0 20 5 | 0 10 0 10 1 | 0 5 0 2 | * 2 *
.. xo ox3oo3oo3oo&#x ♦ 2 5 | 0 1 10 10 | 0 0 5 20 10 | 0 0 10 20 5 | 0 0 10 10 1 | 0 0 5 2 | * * 2
oxx xoo3ooo3ooo3ooo&#x → height(1,2) = height(1,3) = sqrt(7/20) = 0.591608 height(2,3) = 1 o.. o..3o..3o..3o.. | 5 * * ♦ 4 2 2 0 0 0 | 6 1 8 2 1 8 0 | 4 4 12 1 8 4 12 | 1 6 8 4 12 6 8 | 4 2 6 8 4 2 | 1 4 2 1 .o. .o.3.o.3.o.3.o. | * 2 * | 0 5 0 1 1 0 | 0 5 10 5 0 0 1 | 0 10 10 5 10 0 0 | 0 10 5 10 10 0 0 | 5 1 10 5 0 0 | 1 5 1 0 ..o ..o3..o3..o3..o | * * 2 | 0 0 5 0 1 1 | 0 0 0 5 5 10 1 | 0 0 0 5 10 10 10 | 0 0 0 10 10 10 5 | 0 0 10 5 5 1 | 0 5 1 1 -----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+-------- ... x.. ... ... ... | 2 0 0 | 10 * * * * * ♦ 3 0 2 0 0 2 0 | 3 1 6 0 2 1 6 | 1 3 6 1 6 3 6 | 3 2 3 6 3 2 | 1 3 2 1 oo. oo.3oo.3oo.3oo.&#x | 1 1 0 | * 10 * * * * | 0 1 4 1 0 0 0 | 0 4 6 1 4 0 0 | 0 6 4 4 6 0 0 | 4 1 6 4 0 0 | 1 4 1 0 o.o o.o3o.o3o.o3o.o&#x | 1 0 1 | * * 10 * * * | 0 0 0 1 1 4 0 | 0 0 0 1 4 4 6 | 0 0 0 4 6 6 4 | 0 0 6 4 4 1 | 0 4 1 1 .x. ... ... ... ... | 0 2 0 | * * * 1 * * | 0 5 0 0 0 0 1 | 0 10 0 5 0 0 0 | 0 10 0 10 0 0 0 | 5 0 10 0 0 0 | 1 5 0 0 .oo .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * * 2 * | 0 0 0 5 0 0 1 | 0 0 0 5 10 0 0 | 0 0 0 10 10 0 0 | 0 0 10 5 0 0 | 0 5 1 0 ..x ... ... ... ... | 0 0 2 | * * * * * 1 | 0 0 0 0 5 0 1 | 0 0 0 5 0 10 0 | 0 0 0 10 0 10 0 | 0 0 10 0 5 0 | 0 5 0 1 -----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+-------- ... x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 0 | 10 * * * * * * ♦ 2 0 2 0 0 0 2 | 1 1 4 0 2 1 4 | 2 2 1 4 2 2 | 1 2 2 1 ox. ... ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 5 * * * * * | 0 4 0 1 0 0 0 | 0 6 0 4 0 0 0 | 4 0 6 0 0 0 | 1 4 0 0 ... xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * * 20 * * * * | 0 1 3 0 1 0 0 | 0 3 3 1 3 0 0 | 3 1 3 3 0 0 | 1 3 1 0 ooo ooo3ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * 10 * * * | 0 0 0 1 4 0 0 | 0 0 0 4 6 0 0 | 0 0 6 4 0 0 | 0 4 1 0 o.x ... ... ... ...&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 5 * * | 0 0 0 1 0 4 0 | 0 0 0 4 0 6 0 | 0 0 6 0 4 0 | 0 4 0 1 ... x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * * * 20 * | 0 0 0 0 1 1 3 | 0 0 0 1 3 3 3 | 0 0 3 3 3 1 | 0 3 1 1 .xx ... ... ... ...&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * 1 ♦ 0 0 0 5 0 0 0 | 0 0 0 10 0 0 0 | 0 0 10 0 0 0 | 0 5 0 0 -----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+-------- ... x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 | 5 * * * * * * ♦ 1 0 2 0 0 0 2 | 1 2 0 2 1 2 | 1 1 2 1 ox. xo. ... ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 2 0 0 0 0 | * 10 * * * * * | 0 3 0 1 0 0 0 | 3 0 3 0 0 0 | 1 3 0 0 ... xo.3oo. ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 0 3 0 0 0 0 | * * 20 * * * * | 0 1 2 0 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 oxx ... ... ... ...&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 1 0 2 1 0 1 | * * * 5 * * * ♦ 0 0 0 4 0 0 0 | 0 0 6 0 0 0 | 0 4 0 0 ... xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 0 1 2 0 1 0 | * * * * 20 * * | 0 0 0 1 3 0 0 | 0 0 3 3 0 0 | 0 3 1 0 o.x x.o ... ... ...&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 0 0 2 2 0 | * * * * * 10 * | 0 0 0 1 0 3 0 | 0 0 3 0 3 0 | 0 3 0 1 ... x.o3o.o ... ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 | 1 0 0 0 0 3 0 | * * * * * * 20 | 0 0 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1 -----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+-------- ... x..3o..3o..3o.. ♦ 5 0 0 | 10 0 0 0 0 0 | 10 0 0 0 0 0 0 | 5 0 0 0 0 0 0 | 1 * * * * * * | 0 2 0 0 0 2 | 1 0 2 1 ox. xo.3oo. ... ...&#x ♦ 3 2 0 | 3 6 0 1 0 0 | 1 3 6 0 0 0 0 | 0 3 2 0 0 0 0 | * 10 * * * * * | 2 0 1 0 0 0 | 1 2 0 0 ... xo.3oo.3oo. ...&#x ♦ 4 1 0 | 6 4 0 0 0 0 | 4 0 6 0 0 0 0 | 1 0 4 0 0 0 0 | * * 10 * * * * | 1 1 0 1 0 0 | 1 1 1 0 oxx xoo ... ... ...&#x ♦ 2 2 2 | 1 4 4 1 2 1 | 0 2 2 4 2 2 1 | 0 1 0 2 2 1 0 | * * * 10 * * * | 0 0 3 0 0 0 | 0 3 0 0 ... xoo3ooo ... ...&#x ♦ 3 1 1 | 3 3 3 0 1 0 | 1 0 3 3 0 3 0 | 0 0 1 0 3 0 1 | * * * * 20 * * | 0 0 1 2 0 0 | 0 2 1 0 o.x x.o3o.o ... ...&#x ♦ 3 0 2 | 3 0 6 0 0 1 | 1 0 0 0 3 6 0 | 0 0 0 0 0 3 2 | * * * * * 10 * | 0 0 1 0 2 0 | 0 2 0 1 ... x.o3o.o3o.o ...&#x ♦ 4 0 1 | 6 0 4 0 0 0 | 4 0 0 0 0 6 0 | 1 0 0 0 0 0 4 | * * * * * * 10 | 0 0 0 1 1 1 | 0 1 1 1 -----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+-------- ox. xo.3oo.3oo. ...&#x ♦ 4 2 0 | 6 8 0 1 0 0 | 4 4 12 0 0 0 0 | 1 6 8 0 0 0 0 | 0 4 2 0 0 0 0 | 5 * * * * * | 1 1 0 0 ... xo.3oo.3oo.3oo.&#x ♦ 5 1 0 | 10 5 0 0 0 0 | 10 0 10 0 0 0 0 | 5 0 10 0 0 0 0 | 1 0 5 0 0 0 0 | * 2 * * * * | 1 0 1 0 oxx xoo3ooo ... ...&#x ♦ 3 2 2 | 3 6 6 1 2 1 | 1 3 6 6 3 6 1 | 0 3 2 3 6 3 2 | 0 1 0 3 2 1 0 | * * 10 * * * | 0 2 0 0 ... xoo3ooo3ooo ...&#x ♦ 4 1 1 | 6 4 4 0 1 0 | 4 0 6 4 0 6 0 | 1 0 4 0 6 0 4 | 0 0 1 0 4 0 1 | * * * 10 * * | 0 1 1 0 o.x x.o3o.o3o.o ...&#x ♦ 4 0 2 | 6 0 8 0 0 1 | 4 0 0 0 4 12 0 | 1 0 0 0 0 6 8 | 0 0 0 0 0 4 2 | * * * * 5 * | 0 1 0 1 ... x.o3o.o3o.o3o.o&#x ♦ 5 0 1 | 10 0 5 0 0 0 | 10 0 0 0 0 10 0 | 5 0 0 0 0 0 10 | 1 0 0 0 0 0 5 | * * * * * 2 | 0 0 1 1 -----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+-------- ox. xo.3oo.3oo.3oo.&#x ♦ 5 2 0 | 10 10 0 1 0 0 | 10 5 20 0 0 0 0 | 5 10 20 0 0 0 0 | 1 10 10 0 0 0 0 | 5 2 0 0 0 0 | 1 * * * oxx xoo3ooo3ooo ...&#x ♦ 4 2 2 | 6 8 8 1 2 1 | 4 4 12 8 4 12 1 | 1 6 8 4 12 6 8 | 0 4 2 6 8 4 2 | 1 0 4 2 1 0 | * 5 * * ... xoo3ooo3ooo3ooo&#x ♦ 5 1 1 | 10 5 5 0 1 0 | 10 0 10 5 0 10 0 | 5 0 10 0 10 0 10 | 1 0 5 0 10 0 5 | 0 1 0 5 0 1 | * * 2 * o.x x.o3o.o3o.o3o.o&#x ♦ 5 0 2 | 10 0 10 0 0 1 | 10 0 0 0 5 20 0 | 5 0 0 0 0 10 20 | 1 0 0 0 0 10 10 | 0 0 0 0 5 2 | * * * 1
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