Acronym | tratetpy |
Name |
(triangle,tetrahedron)-duoprism pyramid, vertex-pyramid of bril |
Circumradius | sqrt(6/7) = 0.925820 |
Face vector | 13, 42, 64, 55, 28, 8 |
Confer |
|
Incidence matrix according to Dynkin symbol
ox3oo ox3oo3oo&#x → height = sqrt(7/24) = 0.540062
(pt || tratet)
o.3o. o.3o.3o. | 1 * ♦ 12 0 0 | 12 18 0 0 0 | 4 16 12 0 0 0 | 6 12 3 0 0 | 4 3 0
.o3.o .o3.o3.o | * 12 | 1 2 3 | 2 3 1 6 3 | 1 6 3 3 6 1 | 3 6 1 3 2 | 3 2 1
------------------+------+----------+---------------+----------------+------------+------
oo3oo oo3oo3oo&#x | 1 1 | 12 * * | 2 3 0 0 0 | 1 6 3 0 0 0 | 3 6 1 0 0 | 3 2 0
.x .. .. .. .. | 0 2 | * 12 * | 1 0 1 3 0 | 1 3 0 3 3 0 | 3 3 0 3 1 | 3 1 1
.. .. .x .. .. | 0 2 | * * 18 | 0 1 0 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
------------------+------+----------+---------------+----------------+------------+------
ox .. .. .. ..&#x | 1 2 | 2 1 0 | 12 * * * * | 1 3 0 0 0 0 | 3 3 0 0 0 | 3 1 0
.. .. ox .. ..&#x | 1 2 | 2 0 1 | * 18 * * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.x3.o .. .. .. | 0 3 | 0 3 0 | * * 4 * * | 1 0 0 3 0 0 | 3 0 0 3 0 | 3 0 1
.x .. .x .. .. | 0 4 | 0 2 2 | * * * 18 * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x3.o .. | 0 3 | 0 0 3 | * * * * 12 | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
------------------+------+----------+---------------+----------------+------------+------
ox3oo .. .. ..&#x ♦ 1 3 | 3 3 0 | 3 0 1 0 0 | 4 * * * * * | 3 0 0 0 0 | 3 0 0
ox .. ox .. ..&#x ♦ 1 4 | 4 2 2 | 2 2 0 1 0 | * 18 * * * * | 1 2 0 0 0 | 2 1 0
.. .. ox3oo ..&#x ♦ 1 3 | 3 0 3 | 0 3 0 0 1 | * * 12 * * * | 0 2 1 0 0 | 1 2 0
.x3.o .x .. .. ♦ 0 6 | 0 6 3 | 0 0 2 3 0 | * * * 6 * * | 1 0 0 2 0 | 2 0 1
.x .. .x3.o .. ♦ 0 6 | 0 3 6 | 0 0 0 3 2 | * * * * 12 * | 0 1 0 1 1 | 1 1 1
.. .. .x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 0 0 4 | * * * * * 3 | 0 0 1 0 2 | 0 2 1
------------------+------+----------+---------------+----------------+------------+------
ox3oo ox .. ..&#x ♦ 1 6 | 6 6 3 | 6 3 2 3 0 | 2 3 0 1 0 0 | 6 * * * * | 2 0 0
ox .. ox3oo ..&#x ♦ 1 6 | 6 3 6 | 3 6 0 3 2 | 0 3 2 0 1 0 | * 12 * * * | 1 1 0
.. .. ox3oo3oo&#x ♦ 1 4 | 4 0 6 | 0 6 0 0 4 | 0 0 4 0 0 1 | * * 3 * * | 0 2 0
.x3.o .x3.o .. ♦ 0 9 | 0 9 9 | 0 0 3 9 3 | 0 0 0 3 3 0 | * * * 4 * | 1 0 1
.x .. .x3.o3.o ♦ 0 8 | 0 4 12 | 0 0 0 6 8 | 0 0 0 0 4 2 | * * * * 3 | 0 1 1
------------------+------+----------+---------------+----------------+------------+------
ox3oo ox3oo ..&#x ♦ 1 9 | 9 9 9 | 9 9 3 9 3 | 3 9 3 3 3 0 | 3 3 0 1 0 | 4 * *
ox .. ox3oo3oo&#x ♦ 1 8 | 8 4 12 | 4 12 0 6 8 | 0 6 8 0 4 2 | 0 4 2 0 1 | * 3 *
.x3.o .x3.o3.o ♦ 0 12 | 0 12 18 | 0 0 4 18 12 | 0 0 0 6 12 3 | 0 0 0 4 3 | * * 1
xoo oxo xxo3ooo&#x → height(1,2) = 1/sqrt(2) = 0.707107 height(1,3) = height(2,3) = sqrt(5/12) = 0.645497 o.. o.. o..3o.. | 6 * * | 1 2 2 1 0 0 0 | 2 1 2 1 4 1 2 2 0 0 0 0 | 1 1 4 2 2 2 1 2 1 4 0 0 0 | 2 2 1 1 1 4 2 2 0 | 1 2 2 1 .o. .o. .o.3.o. | * 6 * | 0 0 2 0 1 2 1 | 0 0 1 2 4 0 0 2 2 1 1 2 | 0 1 2 4 2 0 0 1 2 4 1 2 1 | 2 1 2 0 1 2 4 2 1 | 1 2 1 2 ..o ..o ..o3..o | * * 1 | 0 0 0 6 0 0 6 | 0 0 0 0 0 3 6 12 0 0 3 6 | 0 0 0 0 0 3 2 6 6 12 0 3 2 | 0 0 0 1 3 6 6 4 1 | 0 3 2 2 -------------------+-------+----------------+---------------------------+----------------------------+-------------------+-------- x.. ... ... ... | 2 0 0 | 3 * * * * * * | 2 0 2 0 0 1 0 0 0 0 0 0 | 1 1 4 0 0 2 0 2 0 0 0 0 0 | 2 2 0 1 1 4 0 0 0 | 1 2 2 0 ... ... x.. ... | 2 0 0 | * 6 * * * * * | 1 1 0 0 2 0 1 0 0 0 0 0 | 1 0 2 1 2 1 1 0 0 2 0 0 0 | 1 2 1 1 0 2 1 2 0 | 1 1 2 1 oo. oo. oo.3oo.&#x | 1 1 0 | * * 12 * * * * | 0 0 1 1 2 0 0 1 0 0 0 0 | 0 1 2 2 1 0 0 1 1 2 0 0 0 | 2 1 1 0 1 2 2 1 0 | 1 2 1 1 o.o o.o o.o3o.o&#x | 1 0 1 | * * * 6 * * * | 0 0 0 0 0 1 2 2 0 0 0 0 | 0 0 0 0 0 2 1 2 1 4 0 0 0 | 0 0 0 1 1 4 2 2 0 | 0 2 2 1 ... .x. ... ... | 0 2 0 | * * * * 3 * * | 0 0 0 2 0 0 0 0 2 0 1 0 | 0 1 0 4 0 0 0 0 2 0 1 2 0 | 2 0 2 0 1 0 4 0 1 | 1 2 0 2 ... ... .x. ... | 0 2 0 | * * * * * 6 * | 0 0 0 0 2 0 0 0 1 1 0 1 | 0 0 1 2 2 0 0 0 0 2 1 1 1 | 1 1 2 0 0 1 2 2 1 | 1 1 1 2 .oo .oo .oo3.oo&#x | 0 1 1 | * * * * * * 6 | 0 0 0 0 0 0 0 2 0 0 1 2 | 0 0 0 0 0 0 0 1 2 4 0 2 1 | 0 0 0 0 1 2 4 2 1 | 0 2 1 2 -------------------+-------+----------------+---------------------------+----------------------------+-------------------+-------- x.. ... x.. ... | 4 0 0 | 2 2 0 0 0 0 0 | 3 * * * * * * * * * * * | 1 0 2 0 0 1 0 0 0 0 0 0 0 | 1 2 0 1 0 2 0 0 0 | 1 1 2 0 ... ... x..3o.. | 3 0 0 | 0 3 0 0 0 0 0 | * 2 * * * * * * * * * * | 1 0 0 0 2 0 1 0 0 0 0 0 0 | 0 2 1 1 0 0 0 2 0 | 1 0 2 1 xo. ... ... ...&#x | 2 1 0 | 1 0 2 0 0 0 0 | * * 6 * * * * * * * * * | 0 1 2 0 0 0 0 1 0 0 0 0 0 | 2 1 0 0 1 2 0 0 0 | 1 2 1 0 ... ox. ... ...&#x | 1 2 0 | 0 0 2 0 1 0 0 | * * * 6 * * * * * * * * | 0 1 0 2 0 0 0 0 1 0 0 0 0 | 2 0 1 0 1 0 2 0 0 | 1 2 0 1 ... ... xx. ...&#x | 2 2 0 | 0 1 2 0 0 1 0 | * * * * 12 * * * * * * * | 0 0 1 1 1 0 0 0 0 1 0 0 0 | 1 1 1 0 0 1 1 1 0 | 1 1 1 1 x.o ... ... ...&#x | 2 0 1 | 1 0 0 2 0 0 0 | * * * * * 3 * * * * * * | 0 0 0 0 0 2 0 2 0 0 0 0 0 | 0 0 0 1 1 4 0 0 0 | 1 1 0 2 ... ... x.o ...&#x | 2 0 1 | 0 1 0 2 0 0 0 | * * * * * * 6 * * * * * | 0 0 0 0 0 1 1 0 0 2 0 0 0 | 0 0 0 1 0 2 1 2 0 | 0 1 2 1 ooo ooo ooo3ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 | * * * * * * * 12 * * * * | 0 0 0 0 0 0 0 1 1 2 0 0 0 | 0 0 0 0 1 2 2 1 0 | 0 2 1 1 ... .x. .x. ... | 0 4 0 | 0 0 0 0 2 2 0 | * * * * * * * * 3 * * * | 0 0 0 2 0 0 0 0 0 0 1 1 0 | 1 0 2 0 0 0 2 0 1 | 1 1 0 2 ... ... .x.3.o. | 0 3 0 | 0 0 0 0 0 3 0 | * * * * * * * * * 2 * * | 0 0 0 0 2 0 0 0 0 0 1 0 1 | 0 1 2 0 0 0 0 2 1 | 1 0 1 2 ... .xo ... ...&#x | 0 2 1 | 0 0 0 0 1 0 2 | * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 2 0 0 2 0 | 0 0 0 0 1 0 4 0 1 | 0 2 0 2 ... ... .xo ...&#x | 0 2 1 | 0 0 0 0 0 1 2 | * * * * * * * * * * * 6 | 0 0 0 0 0 0 0 0 0 2 0 1 1 | 0 0 0 0 0 1 2 2 1 | 0 1 1 2 -------------------+-------+----------------+---------------------------+----------------------------+-------------------+-------- x.. ... x..3o.. ♦ 6 0 0 | 3 6 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * | 0 2 0 1 0 0 0 0 0 | 1 0 2 0 xo. ox. ... ...&#x ♦ 2 2 0 | 1 0 4 0 1 0 0 | 0 0 2 2 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * | 2 0 0 0 1 0 0 0 0 | 1 2 0 0 xo. ... xx. ...&#x ♦ 4 2 0 | 2 2 4 0 0 1 0 | 1 0 2 0 2 0 0 0 0 0 0 0 | * * 6 * * * * * * * * * * | 1 1 0 0 0 1 0 0 0 | 1 1 1 0 ... ox. xx. ...&#x ♦ 2 4 0 | 0 1 4 0 2 2 0 | 0 0 0 2 2 0 0 0 1 0 0 0 | * * * 6 * * * * * * * * * | 1 0 1 0 0 0 1 0 0 | 1 1 0 1 ... ... xx.3oo.&#x ♦ 3 3 0 | 0 3 3 0 0 3 0 | 0 1 0 0 3 0 0 0 0 1 0 0 | * * * * 4 * * * * * * * * | 0 1 1 0 0 0 0 1 0 | 1 0 1 1 x.o ... x.o ...&#x ♦ 4 0 1 | 2 2 0 4 0 0 0 | 1 0 0 0 0 2 2 0 0 0 0 0 | * * * * * 3 * * * * * * * | 0 0 0 1 0 2 0 0 0 | 0 1 2 0 ... ... x.o3o.o&#x ♦ 3 0 1 | 0 3 0 3 0 0 0 | 0 1 0 0 0 0 3 0 0 0 0 0 | * * * * * * 2 * * * * * * | 0 0 0 1 0 0 0 2 0 | 0 0 2 1 xoo ... ... ...&#x ♦ 2 1 1 | 1 0 2 2 0 0 1 | 0 0 1 0 0 1 0 2 0 0 0 0 | * * * * * * * 6 * * * * * | 0 0 0 0 1 2 0 0 0 | 0 2 1 0 ... oxo ... ...&#x ♦ 1 2 1 | 0 0 2 1 1 0 2 | 0 0 0 1 0 0 0 2 0 0 1 0 | * * * * * * * * 6 * * * * | 0 0 0 0 1 0 2 0 0 | 0 2 0 1 ... ... xxo ...&#x ♦ 2 2 1 | 0 1 2 2 0 1 2 | 0 0 0 0 1 0 1 2 0 0 0 1 | * * * * * * * * * 12 * * * | 0 0 0 0 0 1 1 1 0 | 0 1 1 1 ... .x. .x.3.o. ♦ 0 6 0 | 0 0 0 0 3 6 0 | 0 0 0 0 0 0 0 0 3 2 0 0 | * * * * * * * * * * 1 * * | 0 0 2 0 0 0 0 0 1 | 1 0 0 2 ... .xo .xo ...&#x ♦ 0 4 1 | 0 0 0 0 2 2 4 | 0 0 0 0 0 0 0 0 1 0 2 2 | * * * * * * * * * * * 3 * | 0 0 0 0 0 0 2 0 1 | 0 1 0 2 ... ... .xo3.oo&#x ♦ 0 3 1 | 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 1 0 3 | * * * * * * * * * * * * 2 | 0 0 0 0 0 0 0 2 1 | 0 0 1 2 -------------------+-------+----------------+---------------------------+----------------------------+-------------------+-------- xo. ox. xx. ...&#x ♦ 4 4 0 | 2 2 8 0 2 2 0 | 1 0 4 4 4 0 0 0 1 0 0 0 | 0 2 2 2 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * | 1 1 0 0 xo. ... xx.3oo.&#x ♦ 6 3 0 | 3 6 6 0 0 3 0 | 3 2 3 0 6 0 0 0 0 1 0 0 | 1 0 3 0 2 0 0 0 0 0 0 0 0 | * 2 * * * * * * * | 1 0 1 0 ... ox. xx.3oo.&#x ♦ 3 6 0 | 0 3 6 0 3 6 0 | 0 1 0 3 6 0 0 0 3 2 0 0 | 0 0 0 3 2 0 0 0 0 0 1 0 0 | * * 2 * * * * * * | 1 0 0 1 x.o ... x.o3o.o&#x ♦ 6 0 1 | 3 6 0 6 0 0 0 | 3 2 0 0 0 3 6 0 0 0 0 0 | 1 0 0 0 0 3 2 0 0 0 0 0 0 | * * * 1 * * * * * | 0 0 2 0 xoo oxo ... ...&#x ♦ 2 2 1 | 1 0 4 2 1 0 2 | 0 0 2 2 0 1 0 4 0 0 1 0 | 0 1 0 0 0 0 0 2 2 0 0 0 0 | * * * * 3 * * * * | 0 2 0 0 xoo ... xxo ...&#x ♦ 4 2 1 | 2 2 4 4 0 1 2 | 1 0 2 0 2 2 2 4 0 0 0 1 | 0 0 1 0 0 1 0 2 0 2 0 0 0 | * * * * * 6 * * * | 0 1 1 0 ... oxo xxo ...&#x ♦ 2 4 1 | 0 1 4 2 2 2 4 | 0 0 0 2 2 0 1 4 1 0 2 2 | 0 0 0 1 0 0 0 0 2 2 0 1 0 | * * * * * * 6 * * | 0 1 0 1 ... ... xxo3ooo&#x ♦ 3 3 1 | 0 3 3 3 0 3 3 | 0 1 0 0 3 0 3 3 0 1 0 3 | 0 0 0 0 1 0 1 0 0 3 0 0 1 | * * * * * * * 4 * | 0 0 1 1 ... .xo .xo3.oo&#x ♦ 0 6 1 | 0 0 0 0 3 6 6 | 0 0 0 0 0 0 0 0 3 2 3 6 | 0 0 0 0 0 0 0 0 0 0 1 3 2 | * * * * * * * * 1 | 0 0 0 2 -------------------+-------+----------------+---------------------------+----------------------------+-------------------+-------- xo. ox. xx.3oo.&#x ♦ 6 6 0 | 3 6 12 0 3 6 0 | 3 2 6 6 12 0 0 0 3 2 0 0 | 1 3 6 6 4 0 0 0 0 0 1 0 0 | 3 2 2 0 0 0 0 0 0 | 1 * * * xoo oxo xxo ...&#x ♦ 4 4 1 | 2 2 8 4 2 2 4 | 1 0 4 4 4 2 2 8 1 0 2 2 | 0 2 2 2 0 1 0 4 4 4 0 1 0 | 1 0 0 0 2 2 2 0 0 | * 3 * * xoo ... xxo3ooo&#x ♦ 6 3 1 | 3 6 6 6 0 3 3 | 3 2 3 0 6 3 6 6 0 1 0 3 | 1 0 3 0 2 3 2 3 0 6 0 0 1 | 0 1 0 1 0 3 0 2 0 | * * 2 * ... oxo xxo3ooo&#x ♦ 3 6 1 | 0 3 6 3 3 6 6 | 0 1 0 3 6 0 3 6 3 2 3 6 | 0 0 0 3 2 0 1 0 3 6 1 3 2 | 0 0 1 0 0 0 3 2 1 | * * * 2
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