Acronym | rapesc |
Name |
rectified-pentachoric scalene, rectified-pentachoron-pyramid pyramid, line atop fully orthogonal rectified pentachoron |
Circumradius | sqrt(2/3) = 0.816497 |
Face vector | 12, 51, 100, 100, 51, 12 |
Confer |
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It might be worth noting that 12 copies of this polypeton can be aligned around their special edge with A5 around symmetry, then forming a dotet.
Incidence matrix according to Dynkin symbol
xo oo3ox3oo3oo&#x → height = sqrt(3/20) = 0.387298 (pyramid product of line with rap) o. o.3o.3o.3o. | 2 * ♦ 1 10 0 | 10 30 0 0 | 30 10 20 0 0 | 10 20 5 5 0 | 5 5 1 .o .o3.o3.o3.o | * 10 ♦ 0 2 6 | 1 12 3 6 | 6 6 12 3 2 | 3 6 6 4 1 | 3 2 2 ------------------+------+---------+-------------+--------------+---------------+------ x. .. .. .. .. | 2 0 | 1 * * ♦ 10 0 0 0 | 30 0 0 0 0 | 10 20 0 0 0 | 5 5 0 oo oo3oo3oo3oo&#x | 1 1 | * 20 * ♦ 1 6 0 0 | 6 3 6 0 0 | 3 6 3 2 0 | 3 2 1 .. .. .x .. .. | 0 2 | * * 30 | 0 2 1 2 | 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 ------------------+------+---------+-------------+--------------+---------------+------ xo .. .. .. ..&#x | 2 1 | 1 2 0 | 10 * * * ♦ 6 0 0 0 0 | 3 6 0 0 0 | 3 2 0 .. .. ox .. ..&#x | 1 2 | 0 2 1 | * 60 * * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 .. .o3.x .. .. | 0 3 | 0 0 3 | * * 10 * | 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 .. .. .x3.o .. | 0 3 | 0 0 3 | * * * 20 | 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 ------------------+------+---------+-------------+--------------+---------------+------ xo .. ox .. ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 0 | 30 * * * * | 1 2 0 0 0 | 2 1 0 .. oo3ox .. ..&#x ♦ 1 3 | 0 3 3 | 0 3 1 0 | * 20 * * * | 1 0 2 0 0 | 2 0 1 .. .. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0 3 0 1 | * * 40 * * | 0 1 1 1 0 | 1 1 1 .. .o3.x3.o .. ♦ 0 6 | 0 0 12 | 0 0 4 4 | * * * 5 * | 0 0 2 0 1 | 1 0 2 .. .. .x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * 5 | 0 0 0 2 1 | 0 1 2 ------------------+------+---------+-------------+--------------+---------------+------ xo oo3ox .. ..&#x ♦ 2 3 | 1 6 3 | 3 6 1 0 | 3 2 0 0 0 | 10 * * * * | 2 0 0 xo .. ox3oo ..&#x ♦ 2 3 | 1 6 3 | 3 6 0 1 | 3 0 2 0 0 | * 20 * * * | 1 1 0 .. oo3ox3oo ..&#x ♦ 1 6 | 0 6 12 | 0 12 4 4 | 0 4 4 1 0 | * * 10 * * | 1 0 1 .. .. ox3oo3oo&#x ♦ 1 4 | 0 4 6 | 0 6 0 4 | 0 0 4 0 1 | * * * 10 * | 0 1 1 .. .o3.x3.o3.o ♦ 0 10 | 0 0 30 | 0 0 10 20 | 0 0 0 5 5 | * * * * 1 | 0 0 2 ------------------+------+---------+-------------+--------------+---------------+------ xo oo3ox3oo ..&#x ♦ 2 6 | 1 12 12 | 6 24 4 4 | 12 8 8 1 0 | 4 4 2 0 0 | 5 * * xo .. ox3oo3oo&#x ♦ 2 4 | 1 8 6 | 4 12 0 4 | 6 0 8 0 1 | 0 4 0 2 0 | * 5 * .. oo3ox3oo3oo&#x ♦ 1 10 | 0 10 30 | 0 30 10 20 | 0 10 20 5 5 | 0 0 5 5 1 | * * 2
ooo3oxo3ooo3ooo&#x → height(1,2) = height(2,3) = sqrt(2/5) = 0.632456 height(1,3) = 1 o..3o..3o..3o.. | 1 * * ♦ 10 1 0 0 | 30 10 0 0 0 | 10 20 30 0 0 0 0 | 5 5 10 20 0 0 0 | 1 5 5 0 .o.3.o.3.o.3.o. | * 10 * ♦ 1 0 6 1 | 6 1 3 6 6 | 3 6 6 3 2 3 6 | 3 2 3 6 1 3 2 | 1 3 2 1 ..o3..o3..o3..o | * * 1 ♦ 0 1 0 10 | 0 10 0 0 30 | 0 0 30 0 0 10 20 | 0 0 10 20 0 5 5 | 0 5 5 1 -------------------+--------+------------+----------------+--------------------+-----------------+-------- oo.3oo.3oo.3oo.&#x | 1 1 0 | 10 * * * ♦ 6 1 0 0 0 | 3 6 6 0 0 0 0 | 3 2 3 6 0 0 0 | 1 3 2 0 o.o3o.o3o.o3o.o&#x | 1 0 1 | * 1 * * ♦ 0 10 0 0 0 | 0 0 30 0 0 0 0 | 0 0 10 20 0 0 0 | 0 5 5 0 ... .x. ... ... | 0 2 0 | * * 30 * | 1 0 1 2 1 | 1 2 1 2 1 1 2 | 2 1 1 2 1 2 1 | 1 2 1 1 .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * 10 ♦ 0 1 0 0 6 | 0 0 6 0 0 3 6 | 0 0 3 6 0 3 2 | 0 3 2 1 -------------------+--------+------------+----------------+--------------------+-----------------+-------- ... ox. ... ...&#x | 1 2 0 | 2 0 1 0 | 30 * * * * | 1 2 1 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0 ooo3ooo3ooo3ooo&#x | 1 1 1 | 1 1 0 1 | * 10 * * * ♦ 0 0 6 0 0 0 0 | 0 0 3 6 0 0 0 | 0 3 2 0 .o.3.x. ... ... | 0 3 0 | 0 0 3 0 | * * 10 * * | 1 0 0 2 0 1 0 | 2 0 1 0 1 2 0 | 1 2 0 1 ... .x.3.o. ... | 0 3 0 | 0 0 3 0 | * * * 20 * | 0 1 0 1 1 0 1 | 1 1 0 1 1 1 1 | 1 1 1 1 ... .xo ... ...&#x | 0 2 1 | 0 0 1 2 | * * * * 30 | 0 0 1 0 0 1 2 | 0 0 1 2 0 2 1 | 0 2 1 1 -------------------+--------+------------+----------------+--------------------+-----------------+-------- oo.3ox. ... ...&#x ♦ 1 3 0 | 3 0 3 0 | 3 0 1 0 0 | 10 * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0 ... ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3 0 | 3 0 0 1 0 | * 20 * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0 ... oxo ... ...&#x ♦ 1 2 1 | 2 1 1 2 | 1 2 0 0 1 | * * 30 * * * * | 0 0 1 2 0 0 0 | 0 2 1 0 .o.3.x.3.o. ... ♦ 0 6 0 | 0 0 12 0 | 0 0 4 4 0 | * * * 5 * * * | 1 0 0 0 1 1 0 | 1 1 0 1 ... .x.3.o.3.o. ♦ 0 4 0 | 0 0 6 0 | 0 0 0 4 0 | * * * * 5 * * | 0 1 0 0 1 0 1 | 1 0 1 1 .oo3.xo ... ...&#x ♦ 0 3 1 | 0 0 3 3 | 0 0 1 0 3 | * * * * * 10 * | 0 0 1 0 0 2 0 | 0 2 0 1 ... .xo3.oo ...&#x ♦ 0 3 1 | 0 0 3 3 | 0 0 0 1 3 | * * * * * * 20 | 0 0 0 1 0 1 1 | 0 1 1 1 -------------------+--------+------------+----------------+--------------------+-----------------+-------- oo.3ox.3oo. ...&#x ♦ 1 6 0 | 6 0 12 0 | 12 0 4 4 0 | 4 4 0 1 0 0 0 | 5 * * * * * * | 1 1 0 0 ... ox.3oo.3oo.&#x ♦ 1 4 0 | 4 0 6 0 | 6 0 0 4 0 | 0 4 0 0 1 0 0 | * 5 * * * * * | 1 0 1 0 ooo3oxo ... ...&#x ♦ 1 3 1 | 3 1 3 3 | 3 3 1 0 3 | 1 0 3 0 0 1 0 | * * 10 * * * * | 0 2 0 0 ... oxo3ooo ...&#x ♦ 1 3 1 | 3 1 3 3 | 3 3 0 1 3 | 0 1 3 0 0 0 1 | * * * 20 * * * | 0 1 1 0 .o.3.x.3.o.3.o. ♦ 0 10 0 | 0 0 30 0 | 0 0 10 20 0 | 0 0 0 5 5 0 0 | * * * * 1 * * | 1 0 0 1 .oo3.xo3.oo ...&#x ♦ 0 6 1 | 0 0 12 6 | 0 0 4 4 12 | 0 0 0 1 0 4 4 | * * * * * 5 * | 0 1 0 1 ... .xo3.oo3.oo&#x ♦ 0 4 1 | 0 0 6 4 | 0 0 0 4 6 | 0 0 0 0 1 0 4 | * * * * * * 5 | 0 0 1 1 -------------------+--------+------------+----------------+--------------------+-----------------+-------- oo.3ox.3oo.3oo.&#x ♦ 1 10 0 | 10 0 30 0 | 30 0 10 20 0 | 10 20 0 5 5 0 0 | 5 5 0 0 1 0 0 | 1 * * * ooo3oxo3ooo ...&#x ♦ 1 6 1 | 6 1 12 6 | 12 6 4 4 12 | 4 4 12 1 0 4 4 | 1 0 4 4 0 1 0 | * 5 * * ... oxo3ooo3ooo&#x ♦ 1 4 1 | 4 1 6 4 | 6 4 0 4 6 | 0 4 6 0 1 0 4 | 0 1 0 4 0 0 1 | * * 5 * .oo3.xo3.oo3.oo&#x ♦ 0 10 1 | 0 0 30 10 | 0 0 10 20 30 | 0 0 0 5 5 10 20 | 0 0 0 0 1 5 5 | * * * 1
xoo oxo3oox3ooo&#x → height(1,2) = sqrt(3/8) = 0.612372 height(1,3) = 1/2 height(2,3) = sqrt(5/8) = 0.790569 o.. o..3o..3o.. | 2 * * ♦ 1 4 6 0 0 0 | 4 6 6 12 12 0 0 0 0 0 | 6 4 12 4 4 12 6 12 0 0 0 0 | 4 1 4 4 1 6 12 4 4 0 | 1 1 4 4 1 .o. .o.3.o.3.o. | * 4 * ♦ 0 2 0 3 3 0 | 1 6 0 0 6 3 3 3 0 0 | 3 6 0 0 0 3 6 6 1 3 1 0 | 3 2 0 0 0 3 3 6 2 1 | 1 0 3 1 2 ..o ..o3..o3..o | * * 6 ♦ 0 0 2 0 2 4 | 0 0 1 8 4 0 1 4 2 2 | 0 0 4 4 4 2 2 8 0 2 2 1 | 0 0 2 2 2 1 4 4 4 1 | 0 1 2 2 2 -------------------+-------+----------------+-------------------------+-----------------------------+----------------------+---------- x.. ... ... ... | 2 0 0 | 1 * * * * * ♦ 4 0 6 0 0 0 0 0 0 0 | 6 0 12 0 0 12 0 0 0 0 0 0 | 4 0 4 4 0 6 12 0 0 0 | 1 1 4 4 0 oo. oo.3oo.3oo.&#x | 1 1 0 | * 8 * * * * ♦ 1 3 0 0 3 0 0 0 0 0 | 3 3 0 0 0 3 3 3 0 0 0 0 | 3 1 0 0 0 3 3 3 1 0 | 1 0 3 1 1 o.o o.o3o.o3o.o&#x | 1 0 1 | * * 12 * * * ♦ 0 0 1 4 2 0 0 0 0 0 | 0 0 4 2 2 2 1 4 0 0 0 0 | 0 0 2 2 1 1 4 2 2 0 | 0 1 2 2 1 ... .x. ... ... | 0 2 0 | * * * 6 * * | 0 2 0 0 0 2 1 0 0 0 | 1 4 0 0 0 0 2 0 1 2 0 0 | 2 2 0 0 0 1 0 4 0 1 | 1 0 2 0 2 .oo .oo3.oo3.oo&#x | 0 1 1 | * * * * 12 * | 0 0 0 0 2 0 1 2 0 0 | 0 0 0 0 0 1 2 4 0 2 1 0 | 0 0 0 0 0 1 2 4 2 1 | 0 0 2 1 2 ... ... .x. ... | 0 0 2 | * * * * * 12 | 0 0 0 2 0 0 0 1 1 1 | 0 0 1 2 2 0 0 2 0 1 1 1 | 0 0 1 1 2 0 1 2 2 1 | 0 1 1 1 2 -------------------+-------+----------------+-------------------------+-----------------------------+----------------------+---------- xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | 4 * * * * * * * * * ♦ 3 0 0 0 0 3 0 0 0 0 0 0 | 3 0 0 0 0 3 3 0 0 0 | 1 0 3 1 0 ... ox. ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 12 * * * * * * * * | 1 2 0 0 0 0 1 0 0 0 0 0 | 2 1 0 0 0 1 0 2 0 0 | 1 0 2 0 1 x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * 6 * * * * * * * ♦ 0 0 4 0 0 2 0 0 0 0 0 0 | 0 0 2 2 0 1 4 0 0 0 | 0 1 2 2 0 ... ... o.x ...&#x | 1 0 2 | 0 0 2 0 0 1 | * * * 24 * * * * * * | 0 0 1 1 1 0 0 1 0 0 0 0 | 0 0 1 1 1 0 1 1 1 0 | 0 1 1 1 1 ooo ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * 24 * * * * * | 0 0 0 0 0 1 1 2 0 0 0 0 | 0 0 0 0 0 1 2 2 1 0 | 0 0 2 1 1 ... .x.3.o. ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * 4 * * * * | 0 2 0 0 0 0 0 0 1 1 0 0 | 1 2 0 0 0 0 0 2 0 1 | 1 0 1 0 2 ... .xo ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * 6 * * * | 0 0 0 0 0 0 2 0 0 2 0 0 | 0 0 0 0 0 1 0 4 0 1 | 0 0 2 0 2 ... ... .ox ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * 12 * * | 0 0 0 0 0 0 0 2 0 1 1 0 | 0 0 0 0 0 0 1 2 2 1 | 0 0 1 1 2 ... ..o3..x ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 4 * | 0 0 0 2 0 0 0 0 0 1 0 1 | 0 0 1 0 2 0 0 2 0 1 | 0 1 1 0 2 ... ... ..x3..o | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * 4 | 0 0 0 0 2 0 0 0 0 0 1 1 | 0 0 0 1 2 0 0 0 2 1 | 0 1 0 1 2 -------------------+-------+----------------+-------------------------+-----------------------------+----------------------+---------- xo. ox. ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 2 0 0 0 0 0 0 0 0 | 6 * * * * * * * * * * * | 2 0 0 0 0 1 0 0 0 0 | 1 0 2 0 0 ... ox.3oo. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 0 0 1 0 0 0 0 | * 8 * * * * * * * * * * | 1 1 0 0 0 0 0 1 0 0 | 1 0 1 0 1 x.o ... o.x ...&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 2 2 0 0 0 0 0 0 | * * 12 * * * * * * * * * | 0 0 1 1 0 0 1 0 0 0 | 0 1 1 1 0 ... o.o3o.x ...&#x ♦ 1 0 3 | 0 0 3 0 0 3 | 0 0 0 3 0 0 0 0 1 0 | * * * 8 * * * * * * * * | 0 0 1 0 1 0 0 1 0 0 | 0 1 1 0 1 ... ... o.x3o.o&#x ♦ 1 0 3 | 0 0 3 0 0 3 | 0 0 0 3 0 0 0 0 0 1 | * * * * 8 * * * * * * * | 0 0 0 1 1 0 0 0 1 0 | 0 1 0 1 1 xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 1 0 1 0 2 0 0 0 0 0 | * * * * * 12 * * * * * * | 0 0 0 0 0 1 2 0 0 0 | 0 0 2 1 0 ... oxo ... ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 1 0 0 2 0 1 0 0 0 | * * * * * * 12 * * * * * | 0 0 0 0 0 1 0 2 0 0 | 0 0 2 0 1 ... ... oox ...&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 1 2 0 0 1 0 0 | * * * * * * * 24 * * * * | 0 0 0 0 0 0 1 1 1 0 | 0 0 1 1 1 ... .x.3.o.3.o. ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 4 0 0 0 0 | * * * * * * * * 1 * * * | 0 2 0 0 0 0 0 0 0 1 | 1 0 0 0 2 ... .xo3.ox ...&#x ♦ 0 3 3 | 0 0 0 3 6 3 | 0 0 0 0 0 1 3 3 1 0 | * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 2 0 1 | 0 0 1 0 2 ... ... .ox3.oo&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 3 0 1 | * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 2 1 | 0 0 0 1 2 ... ..o3..x3..o ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * 1 | 0 0 0 0 2 0 0 0 0 1 | 0 1 0 0 2 -------------------+-------+----------------+-------------------------+-----------------------------+----------------------+---------- xo. ox.3oo. ...&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 3 6 0 0 0 1 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * | 1 0 1 0 0 ... ox.3oo.3oo.&#x ♦ 1 4 0 | 0 4 0 6 0 0 | 0 6 0 0 0 4 0 0 0 0 | 0 4 0 0 0 0 0 0 1 0 0 0 | * 2 * * * * * * * * | 1 0 0 0 1 x.o o.o3o.x ...&#x ♦ 2 0 3 | 1 0 6 0 0 3 | 0 0 3 6 0 0 0 0 1 0 | 0 0 3 2 0 0 0 0 0 0 0 0 | * * 4 * * * * * * * | 0 1 1 0 0 x.o ... o.x3o.o&#x ♦ 2 0 3 | 1 0 6 0 0 3 | 0 0 3 6 0 0 0 0 0 1 | 0 0 3 0 2 0 0 0 0 0 0 0 | * * * 4 * * * * * * | 0 1 0 1 0 ... o.o3o.x3o.o&#x ♦ 1 0 6 | 0 0 6 0 0 12 | 0 0 0 12 0 0 0 0 4 4 | 0 0 0 4 4 0 0 0 0 0 0 1 | * * * * 2 * * * * * | 0 1 0 0 1 xoo oxo ... ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 2 2 1 0 4 0 1 0 0 0 | 1 0 0 0 0 2 2 0 0 0 0 0 | * * * * * 6 * * * * | 0 0 2 0 0 xoo ... oox ...&#x ♦ 2 1 2 | 1 2 4 0 2 1 | 1 0 2 2 4 0 0 1 0 0 | 0 0 1 0 0 2 0 2 0 0 0 0 | * * * * * * 12 * * * | 0 0 1 1 0 ... oxo3oox ...&#x ♦ 1 3 3 | 0 3 3 3 6 3 | 0 3 0 3 6 1 3 3 1 0 | 0 1 0 1 0 0 3 3 0 1 0 0 | * * * * * * * 8 * * | 0 0 1 0 1 ... ... oox3ooo&#x ♦ 1 1 3 | 0 1 3 0 3 3 | 0 0 0 3 3 0 0 3 0 1 | 0 0 0 0 1 0 0 3 0 0 1 0 | * * * * * * * * 8 * | 0 0 0 1 1 ... .xo3.ox3.oo&#x ♦ 0 4 6 | 0 0 0 6 12 12 | 0 0 0 0 0 4 6 12 4 4 | 0 0 0 0 0 0 0 0 1 4 4 1 | * * * * * * * * * 1 | 0 0 0 0 2 -------------------+-------+----------------+-------------------------+-----------------------------+----------------------+---------- xo. ox.3oo.3oo.&#x ♦ 2 4 0 | 1 8 0 6 0 0 | 4 12 0 0 0 4 0 0 0 0 | 6 8 0 0 0 0 0 0 1 0 0 0 | 4 2 0 0 0 0 0 0 0 0 | 1 * * * * x.o o.o3o.x3o.o&#x ♦ 2 0 6 | 1 0 12 0 0 12 | 0 0 6 24 0 0 0 0 4 4 | 0 0 12 8 8 0 0 0 0 0 0 1 | 0 0 4 4 2 0 0 0 0 0 | * 1 * * * xoo oxo3oox ...&#x ♦ 2 3 3 | 1 6 6 3 6 3 | 3 6 3 6 12 1 3 3 1 0 | 3 2 3 2 0 6 6 6 0 1 0 0 | 1 0 1 0 0 3 3 2 0 0 | * * 4 * * xoo ... oox3ooo&#x ♦ 2 1 3 | 1 2 6 0 3 3 | 1 0 3 6 6 0 0 3 0 1 | 0 0 3 0 2 3 0 6 0 0 1 0 | 0 0 0 1 0 0 3 0 2 0 | * * * 4 * ... oxo3oox3ooo&#x ♦ 1 4 6 | 0 4 6 6 12 12 | 0 6 0 12 12 4 6 12 4 4 | 0 4 0 4 4 0 6 12 1 4 4 1 | 0 1 0 0 1 0 0 4 4 1 | * * * * 2
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