Acronym | penpasc |
Name |
pentachoron-prismatic scalene, pentachoron-prism-pyramid pyramid, line atop fully orthogonal pentachoron prism |
|,>,O device | line pyramid pyramid pyramid prism pyramid pyramid = |>>>|>> |
Circumradius | sqrt(7/8) = 0.935414 |
Face vector | 12, 46, 90, 105, 77, 35, 9 |
Confer |
|
Incidence matrix according to Dynkin symbol
xo ox ox3oo3oo3oo&#x → height = 1/sqrt(10) = 0.316228 (pyramid product of line with penp) o. o. o.3o.3o.3o. | 2 * | 1 10 0 0 | 10 5 20 0 0 | 5 20 10 20 0 0 | 10 20 10 10 0 0 | 10 10 5 2 0 | 5 2 1 .o .o .o3.o3.o3.o | * 10 | 0 2 1 4 | 1 2 8 4 6 | 1 4 8 12 6 4 | 4 6 12 8 4 1 | 6 4 8 2 1 | 4 1 2 ---------------------+------+-----------+----------------+------------------+-----------------+--------------+------ x. .. .. .. .. .. | 2 0 | 1 * * * ♦ 10 0 0 0 0 | 5 20 0 0 0 0 | 10 20 0 0 0 0 | 10 10 0 0 0 | 5 2 0 oo oo oo3oo3oo3oo&#x | 1 1 | * 20 * * | 1 1 4 0 0 | 1 4 4 6 0 0 | 4 6 6 4 0 0 | 6 4 4 1 0 | 4 1 1 .. .x .. .. .. .. | 0 2 | * * 5 * | 0 2 0 4 0 | 1 0 8 0 6 0 | 4 0 12 0 4 0 | 6 0 8 0 1 | 4 0 2 .. .. .x .. .. .. | 0 2 | * * * 20 | 0 0 2 1 3 | 0 1 2 6 3 3 | 1 3 6 6 3 1 | 3 3 6 2 1 | 3 1 2 ---------------------+------+-----------+----------------+------------------+-----------------+--------------+------ xo .. .. .. .. ..&#x | 2 1 | 1 2 0 0 | 10 * * * * | 1 4 0 0 0 0 | 4 6 0 0 0 0 | 6 4 0 0 0 | 4 1 0 .. ox .. .. .. ..&#x | 1 2 | 0 2 1 0 | * 10 * * * | 1 0 4 0 0 0 | 4 0 6 0 0 0 | 6 0 4 0 0 | 4 0 1 .. .. ox .. .. ..&#x | 1 2 | 0 2 0 1 | * * 40 * * | 0 1 1 3 0 0 | 1 3 3 3 0 0 | 3 3 3 1 0 | 3 1 1 .. .x .x .. .. .. | 0 4 | 0 0 2 2 | * * * 10 * | 0 0 2 0 3 0 | 1 0 6 0 3 0 | 3 0 6 0 1 | 3 0 2 .. .. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * * 20 | 0 0 0 2 1 2 | 0 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 ---------------------+------+-----------+----------------+------------------+-----------------+--------------+------ xo ox .. .. .. ..&#x ♦ 2 2 | 1 4 1 0 | 2 2 0 0 0 | 5 * * * * * ♦ 4 0 0 0 0 0 | 6 0 0 0 0 | 4 0 0 xo .. ox .. .. ..&#x ♦ 2 2 | 1 4 0 1 | 2 0 2 0 0 | * 20 * * * * | 1 3 0 0 0 0 | 3 3 0 0 0 | 3 1 0 .. ox ox .. .. ..&#x ♦ 1 4 | 0 4 2 2 | 0 2 2 1 0 | * * 20 * * * | 1 0 3 0 0 0 | 3 0 3 0 0 | 3 0 1 .. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 0 3 | 0 0 3 0 1 | * * * 40 * * | 0 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 .. .x .x3.o .. .. ♦ 0 6 | 0 0 3 6 | 0 0 0 3 2 | * * * * 10 * | 0 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 .. .. .x3.o3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * 10 | 0 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 ---------------------+------+-----------+----------------+------------------+-----------------+--------------+------ xo ox ox .. .. ..&#x ♦ 2 4 | 1 8 2 2 | 4 4 4 1 0 | 2 2 2 0 0 0 | 10 * * * * * | 3 0 0 0 0 | 3 0 0 xo .. ox3oo .. ..&#x ♦ 2 3 | 1 6 0 3 | 3 0 6 0 1 | 0 3 0 2 0 0 | * 20 * * * * | 1 2 0 0 0 | 2 1 0 .. ox ox3oo .. ..&#x ♦ 1 6 | 0 6 3 6 | 0 3 6 3 2 | 0 0 3 2 1 0 | * * 20 * * * | 1 0 2 0 0 | 2 0 1 .. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 0 6 | 0 0 6 0 4 | 0 0 0 4 0 1 | * * * 20 * * | 0 1 1 1 0 | 1 1 1 .. .x .x3.o3.o .. ♦ 0 8 | 0 0 4 12 | 0 0 0 6 8 | 0 0 0 0 4 2 | * * * * 5 * | 0 0 2 0 1 | 1 0 2 .. .. .x3.o3.o3.o ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 5 | * * * * * 2 | 0 0 0 2 1 | 0 1 2 ---------------------+------+-----------+----------------+------------------+-----------------+--------------+------ xo ox ox3oo .. ..&#x ♦ 2 6 | 1 12 3 6 | 6 6 12 3 2 | 3 6 6 4 1 0 | 3 2 2 0 0 0 | 10 * * * * | 2 0 0 xo .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 0 6 | 4 0 12 0 4 | 0 6 0 8 0 1 | 0 4 0 2 0 0 | * 10 * * * | 1 1 0 .. ox ox3oo3oo ..&#x ♦ 1 8 | 0 8 4 12 | 0 4 12 6 8 | 0 0 6 8 4 2 | 0 0 4 2 1 0 | * * 10 * * | 1 0 1 .. .. ox3oo3oo3oo&#x ♦ 1 5 | 0 5 0 10 | 0 0 10 0 10 | 0 0 0 10 0 5 | 0 0 0 5 0 1 | * * * 4 * | 0 1 1 .. .x .x3.o3.o3.o ♦ 0 10 | 0 0 5 20 | 0 0 0 10 20 | 0 0 0 0 10 10 | 0 0 0 0 5 2 | * * * * 1 | 0 0 2 ---------------------+------+-----------+----------------+------------------+-----------------+--------------+------ xo ox ox3oo3oo ..&#x ♦ 2 8 | 1 16 4 12 | 8 8 24 6 8 | 4 12 12 16 4 2 | 6 8 8 4 1 0 | 4 2 2 0 0 | 5 * * xo .. ox3oo3oo3oo&#x ♦ 2 5 | 1 10 0 10 | 5 0 20 0 10 | 0 10 0 20 0 5 | 0 10 0 10 0 1 | 0 5 0 2 0 | * 2 * .. ox ox3oo3oo3oo&#x ♦ 1 10 | 0 10 5 20 | 0 5 20 10 20 | 0 0 10 20 10 10 | 0 0 10 10 5 2 | 0 0 5 2 1 | * * 2
xoo oxx3ooo3ooo3ooo&#x → height(1,2) = height(1,3) = sqrt(7/20) = 0.591608 height(2,3) = 1 o.. o..3o..3o..3o.. | 2 * * | 1 5 5 0 0 0 | 5 10 5 5 10 0 0 0 | 10 10 5 10 10 10 0 0 0 | 10 5 10 10 10 5 0 0 0 | 5 1 10 5 5 1 0 | 1 5 1 1 .o. .o.3.o.3.o.3.o. | * 5 * | 0 2 0 4 1 0 | 1 8 2 0 0 6 4 0 | 4 12 1 8 0 0 4 6 0 | 6 8 4 12 0 0 1 4 0 | 4 2 6 8 0 0 1 | 1 4 2 0 ..o ..o3..o3..o3..o | * * 5 | 0 0 2 0 1 4 | 0 0 2 1 8 0 4 6 | 0 0 1 8 4 12 0 6 4 | 0 0 4 12 6 8 0 4 1 | 0 0 6 8 4 2 1 | 0 4 2 1 -----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+-------- x.. ... ... ... ... | 2 0 0 | 1 * * * * * ♦ 5 0 0 5 0 0 0 0 | 10 0 5 0 10 0 0 0 0 | 10 0 10 0 10 0 0 0 0 | 5 0 10 0 5 0 0 | 1 5 0 1 oo. oo.3oo.3oo.3oo.&#x | 1 1 0 | * 10 * * * * | 1 4 1 0 0 0 0 0 | 4 6 1 4 0 0 0 0 0 | 6 4 4 6 0 0 0 0 0 | 4 1 6 4 0 0 0 | 1 4 1 0 o.o o.o3o.o3o.o3o.o&#x | 1 0 1 | * * 10 * * * | 0 0 1 1 4 0 0 0 | 0 0 1 4 4 6 0 0 0 | 0 0 4 6 6 4 0 0 0 | 0 0 6 4 4 1 0 | 0 4 1 1 ... .x. ... ... ... | 0 2 0 | * * * 10 * * | 0 2 0 0 0 3 1 0 | 1 6 0 2 0 0 3 3 0 | 3 6 1 6 0 0 1 3 0 | 3 2 3 6 0 0 1 | 1 3 2 0 .oo .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * * 5 * | 0 0 2 0 0 0 4 0 | 0 0 1 8 0 0 0 6 0 | 0 0 4 12 0 0 0 4 0 | 0 0 6 8 0 0 1 | 0 4 2 0 ... ..x ... ... ... | 0 0 2 | * * * * * 10 | 0 0 0 0 2 0 1 3 | 0 0 0 2 1 6 0 3 3 | 0 0 1 6 3 6 0 3 1 | 0 0 3 6 3 2 1 | 0 3 2 1 -----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+-------- xo. ... ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | 5 * * * * * * * | 4 0 1 0 0 0 0 0 0 | 6 0 4 0 0 0 0 0 0 | 4 0 6 0 0 0 0 | 1 4 0 0 ... ox. ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 20 * * * * * * | 1 3 0 1 0 0 0 0 0 | 3 3 1 3 0 0 0 0 0 | 3 1 3 3 0 0 0 | 1 3 1 0 ooo ooo3ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * 10 * * * * * | 0 0 1 4 0 0 0 0 0 | 0 0 4 6 0 0 0 0 0 | 0 0 6 4 0 0 0 | 0 4 1 0 x.o ... ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 5 * * * * | 0 0 1 0 4 0 0 0 0 | 0 0 4 0 6 0 0 0 0 | 0 0 6 0 4 0 0 | 0 4 0 1 ... o.x ... ... ...&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 20 * * * | 0 0 0 1 1 3 0 0 0 | 0 0 1 3 3 3 0 0 0 | 0 0 3 3 3 1 0 | 0 3 1 1 ... .x.3.o. ... ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * 10 * * | 0 2 0 0 0 0 2 1 0 | 1 4 0 2 0 0 1 2 0 | 2 2 1 4 0 0 1 | 1 2 2 0 ... .xx ... ... ...&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * 10 * | 0 0 0 2 0 0 0 3 0 | 0 0 1 6 0 0 0 3 0 | 0 0 3 6 0 0 1 | 0 3 1 0 ... ..x3..o ... ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * 10 | 0 0 0 0 0 2 0 1 2 | 0 0 0 2 1 4 0 2 1 | 0 0 1 4 2 2 1 | 0 2 2 1 -----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+-------- xo. ox. ... ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 2 0 0 0 0 0 0 | 10 * * * * * * * * | 3 0 1 0 0 0 0 0 0 | 3 0 3 0 0 0 0 | 1 3 0 0 ... ox.3oo. ... ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 0 0 1 0 0 | * 20 * * * * * * * | 1 2 0 1 0 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0 xoo ... ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 1 0 2 1 0 0 0 0 | * * 5 * * * * * * ♦ 0 0 4 0 0 0 0 0 0 | 0 0 6 0 0 0 0 | 0 4 0 0 ... oxx ... ... ...&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 1 2 0 1 0 1 0 | * * * 20 * * * * * | 0 0 1 3 0 0 0 0 0 | 0 0 3 3 0 0 0 | 0 3 1 0 x.o o.x ... ... ...&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 0 2 2 0 0 0 | * * * * 10 * * * * | 0 0 1 0 3 0 0 0 0 | 0 0 3 0 3 0 0 | 0 3 0 1 ... o.x3o.o ... ...&#x ♦ 1 0 3 | 0 0 3 0 0 3 | 0 0 0 0 3 0 0 1 | * * * * * 20 * * * | 0 0 0 1 1 2 0 0 0 | 0 0 1 2 2 1 0 | 0 2 1 1 ... .x.3.o.3.o. ... ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 4 0 0 | * * * * * * 5 * * | 0 2 0 0 0 0 1 1 0 | 1 2 0 2 0 0 1 | 1 1 2 0 ... .xx3.oo ... ...&#x ♦ 0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 1 3 1 | * * * * * * * 10 * | 0 0 0 2 0 0 0 2 0 | 0 0 1 4 0 0 1 | 0 2 2 0 ... ..x3..o3..o ... ♦ 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 4 | * * * * * * * * 5 | 0 0 0 0 0 2 0 1 1 | 0 0 0 2 1 2 1 | 0 1 2 1 -----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+-------- xo. ox.3oo. ... ...&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 3 6 0 0 0 1 0 0 | 3 2 0 0 0 0 0 0 0 | 10 * * * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0 ... ox.3oo.3oo. ...&#x ♦ 1 4 0 | 0 4 0 6 0 0 | 0 6 0 0 0 4 0 0 | 0 4 0 0 0 0 1 0 0 | * 10 * * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0 xoo oxx ... ... ...&#x ♦ 2 2 2 | 1 4 4 1 2 1 | 2 2 4 2 2 0 1 0 | 1 0 2 2 1 0 0 0 0 | * * 10 * * * * * * | 0 0 3 0 0 0 0 | 0 3 0 0 ... oxx3ooo ... ...&#x ♦ 1 3 3 | 0 3 3 3 3 3 | 0 3 3 0 3 1 3 1 | 0 1 0 3 0 1 0 1 0 | * * * 20 * * * * * | 0 0 1 2 0 0 0 | 0 2 1 0 x.o o.x3o.o ... ...&#x ♦ 2 0 3 | 1 0 6 0 0 3 | 0 0 0 3 6 0 0 1 | 0 0 0 0 3 2 0 0 0 | * * * * 10 * * * * | 0 0 1 0 2 0 0 | 0 2 0 1 ... o.x3o.o3o.o ...&#x ♦ 1 0 4 | 0 0 4 0 0 6 | 0 0 0 0 6 0 0 4 | 0 0 0 0 0 4 0 0 1 | * * * * * 10 * * * | 0 0 0 1 1 1 0 | 0 1 1 1 ... .x.3.o.3.o.3.o. ♦ 0 5 0 | 0 0 0 10 0 0 | 0 0 0 0 0 10 0 0 | 0 0 0 0 0 0 5 0 0 | * * * * * * 1 * * | 0 2 0 0 0 0 1 | 1 0 2 0 ... .xx3.oo3.oo ...&#x ♦ 0 4 4 | 0 0 0 6 4 6 | 0 0 0 0 0 4 6 4 | 0 0 0 0 0 0 1 4 1 | * * * * * * * 5 * | 0 0 0 2 0 0 1 | 0 1 2 0 ... ..x3..o3..o3..o ♦ 0 0 5 | 0 0 0 0 0 10 | 0 0 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 5 | * * * * * * * * 1 | 0 0 0 0 0 2 1 | 0 0 2 1 -----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+-------- xo. ox.3oo.3oo. ...&#x ♦ 2 4 0 | 1 8 0 6 0 0 | 4 12 0 0 0 4 0 0 | 6 8 0 0 0 0 1 0 0 | 4 2 0 0 0 0 0 0 0 | 5 * * * * * * | 1 1 0 0 ... ox.3oo.3oo.3oo.&#x ♦ 1 5 0 | 0 5 0 10 0 0 | 0 10 0 0 0 10 0 0 | 0 10 0 0 0 0 5 0 0 | 0 5 0 0 0 0 1 0 0 | * 2 * * * * * | 1 0 1 0 xoo oxx3ooo ... ...&#x ♦ 2 3 3 | 1 6 6 3 3 3 | 3 6 6 3 6 1 3 1 | 3 2 3 6 3 2 0 1 0 | 1 0 3 2 1 0 0 0 0 | * * 10 * * * * | 0 2 0 0 ... oxx3ooo3ooo ...&#x ♦ 1 4 4 | 0 4 4 6 4 6 | 0 6 4 0 6 4 6 4 | 0 4 0 6 0 4 1 4 1 | 0 1 0 4 0 1 0 1 0 | * * * 10 * * * | 0 1 1 0 x.o o.x3o.o3o.o ...&#x ♦ 2 0 4 | 1 0 8 0 0 6 | 0 0 0 4 12 0 0 4 | 0 0 0 0 6 8 0 0 1 | 0 0 0 0 4 2 0 0 0 | * * * * 5 * * | 0 1 0 1 ... o.x3o.o3o.o3o.o&#x ♦ 1 0 5 | 0 0 5 0 0 10 | 0 0 0 0 10 0 0 10 | 0 0 0 0 0 10 0 0 5 | 0 0 0 0 0 5 0 0 1 | * * * * * 2 * | 0 0 1 1 ... .xx3.oo3.oo3.oo&#x ♦ 0 5 5 | 0 0 0 10 5 10 | 0 0 0 0 0 10 10 10 | 0 0 0 0 0 0 5 10 5 | 0 0 0 0 0 0 1 5 1 | * * * * * * 1 | 0 0 2 0 -----------------------+-------+-----------------+-----------------------+-------------------------+-------------------------+-----------------+-------- xo. ox.3oo.3oo.3oo.&#x ♦ 2 5 0 | 1 10 0 10 0 0 | 5 20 0 0 0 10 0 0 | 10 20 0 0 0 0 5 0 0 | 10 10 0 0 0 0 1 0 0 | 5 2 0 0 0 0 0 | 1 * * * xoo oxx3ooo3ooo ...&#x ♦ 2 4 4 | 1 8 8 6 4 6 | 4 12 8 4 12 4 6 4 | 6 8 4 12 6 8 1 4 1 | 4 2 6 8 4 2 0 1 0 | 1 0 4 2 1 0 0 | * 5 * * ... oxx3ooo3ooo3ooo&#x ♦ 1 5 5 | 0 5 5 10 5 10 | 0 10 5 0 10 10 10 10 | 0 10 0 10 0 10 5 10 5 | 0 5 0 10 0 5 1 5 1 | 0 1 0 5 0 1 1 | * * 2 * x.o o.x3o.o3o.o3o.o&#x ♦ 2 0 5 | 1 0 10 0 0 10 | 0 0 0 5 20 0 0 10 | 0 0 0 0 10 20 0 0 5 | 0 0 0 0 10 10 0 0 1 | 0 0 0 0 5 2 0 | * * * 1
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