Acronym | teta ope (alt.: octarap, tetoct octtric) |
Name |
tetrahedron atop octahedron-prism, octahedron atop rectified-pentachoron, half of dodecateron (its tet-first rotunda), (tet,oct,oct)-trigonic |
Circumradius | sqrt(3)/2 = 0.866025 |
Lace city in approx. ASCII-art |
O t where: t = x3o3o (tet) O O = o3x3o (oct) |
Face vector | 16, 60, 80, 45, 11 |
Confer |
|
Incidence matrix according to Dynkin symbol
ox xo3ox3oo&#x → height = sqrt(3/8) = 0.612372
(tet || ope)
o. o.3o.3o. | 4 * ♦ 3 6 0 0 | 3 3 6 6 0 0 0 | 1 3 3 6 2 0 0 0 | 3 1 2 0
.o .o3.o3.o | * 12 | 0 2 1 4 | 0 2 1 4 4 2 2 | 0 1 4 2 2 2 2 1 | 2 2 1 1
---------------+------+-----------+-------------------+------------------+--------
.. x. .. .. | 2 0 | 6 * * * | 2 0 2 0 0 0 0 | 1 1 0 4 0 0 0 0 | 2 0 2 0
oo oo3oo3oo&#x | 1 1 | * 24 * * | 0 1 1 2 0 0 0 | 0 1 2 2 1 0 0 0 | 2 1 1 0
.x .. .. .. | 0 2 | * * 6 * | 0 2 0 0 4 0 0 | 0 1 4 0 0 2 2 0 | 2 2 0 1
.. .. .x .. | 0 2 | * * * 24 | 0 0 0 1 1 1 1 | 0 0 1 1 1 1 1 1 | 1 1 1 1
---------------+------+-----------+-------------------+------------------+--------
.. x.3o. .. | 3 0 | 3 0 0 0 | 4 * * * * * * | 1 0 0 2 0 0 0 0 | 1 0 2 0
ox .. .. ..&#x | 1 2 | 0 2 1 0 | * 12 * * * * * | 0 1 2 0 0 0 0 0 | 2 1 0 0
.. xo .. ..&#x | 2 1 | 1 2 0 0 | * * 12 * * * * | 0 1 0 2 0 0 0 0 | 2 0 1 0
.. .. ox ..&#x | 1 2 | 0 2 0 1 | * * * 24 * * * | 0 0 1 1 1 0 0 0 | 1 1 1 0
.x .. .x .. | 0 4 | 0 0 2 2 | * * * * 12 * * | 0 0 1 0 0 1 1 0 | 1 1 0 1
.. .o3.x .. | 0 3 | 0 0 0 3 | * * * * * 8 * | 0 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.o | 0 3 | 0 0 0 3 | * * * * * * 8 | 0 0 0 0 1 0 1 1 | 0 1 1 1
---------------+------+-----------+-------------------+------------------+--------
.. x.3o.3o. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
ox xo .. ..&#x ♦ 2 2 | 1 4 1 0 | 0 2 2 0 0 0 0 | * 6 * * * * * * | 2 0 0 0
ox .. ox ..&#x ♦ 1 4 | 0 4 2 2 | 0 2 0 2 1 0 0 | * * 12 * * * * * | 1 1 0 0
.. xo3ox ..&#x ♦ 3 3 | 3 6 0 3 | 1 0 3 3 0 1 0 | * * * 8 * * * * | 1 0 1 0
.. .. ox3oo&#x ♦ 1 3 | 0 3 0 3 | 0 0 0 3 0 0 1 | * * * * 8 * * * | 0 1 1 0
.x .o3.x .. ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 2 0 | * * * * * 4 * * | 1 0 0 1
.x .. .x3.o ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 0 2 | * * * * * * 4 * | 0 1 0 1
.. .o3.x3.o ♦ 0 6 | 0 0 0 12 | 0 0 0 0 0 4 4 | * * * * * * * 2 | 0 0 1 1
---------------+------+-----------+-------------------+------------------+--------
ox xo3ox ..&#x ♦ 3 6 | 3 12 3 6 | 1 6 6 6 3 2 0 | 0 3 3 2 0 1 0 0 | 4 * * *
ox .. ox3oo&#x ♦ 1 6 | 0 6 3 6 | 0 3 0 6 3 0 2 | 0 0 3 0 2 0 1 0 | * 4 * *
.. xo3ox3oo&#x ♦ 4 6 | 6 12 0 12 | 4 0 6 12 0 4 4 | 1 0 0 4 4 0 0 1 | * * 2 *
.x .o3.x3.o ♦ 0 12 | 0 0 6 24 | 0 0 0 0 12 8 8 | 0 0 0 0 0 4 4 2 | * * * 1
ooo3oxx3xoo&#x → height(1,2) = height(1,3) = sqrt(5/8) = 0.790569 height(2,3) = 1 height(1,23) = sqrt(3/8) = 0.612372 o..3o..3o.. | 4 * * | 3 3 3 0 0 0 | 3 3 3 3 3 3 0 0 0 0 0 | 1 1 3 3 3 1 3 0 0 0 0 | 1 1 3 1 0 .o.3.o.3.o. | * 6 * | 0 2 0 4 1 0 | 0 4 1 2 0 0 2 2 4 0 0 | 0 2 2 4 1 0 0 1 2 2 0 | 1 2 2 0 1 ..o3..o3..o | * * 6 | 0 0 2 0 1 4 | 0 0 0 2 4 1 0 0 4 2 2 | 0 0 0 4 1 2 2 0 2 2 1 | 0 2 2 1 1 ---------------+-------+-----------------+---------------------------+------------------------+---------- ... ... x.. | 2 0 0 | 6 * * * * * | 2 0 1 0 0 1 0 0 0 0 0 | 1 0 2 0 1 0 2 0 0 0 0 | 1 0 2 1 0 oo.3oo.3oo.&#x | 1 1 0 | * 12 * * * * | 0 2 1 1 0 0 0 0 0 0 0 | 0 1 2 2 1 0 0 0 0 0 0 | 1 1 2 0 0 o.o3o.o3o.o&#x | 1 0 1 | * * 12 * * * | 0 0 0 1 2 2 0 0 0 0 0 | 0 0 0 2 1 1 2 0 0 0 0 | 0 1 2 1 0 ... .x. ... | 0 2 0 | * * * 12 * * | 0 1 0 0 0 0 1 1 1 0 0 | 0 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 .oo3.oo3.oo&#x | 0 1 1 | * * * * 6 * | 0 0 0 2 0 0 0 0 4 0 0 | 0 0 0 4 1 0 0 0 2 2 0 | 0 2 2 0 1 ... ..x ... | 0 0 2 | * * * * * 12 | 0 0 0 0 1 0 0 0 1 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 ---------------+-------+-----------------+---------------------------+------------------------+---------- ... o..3x.. | 3 0 0 | 3 0 0 0 0 0 | 4 * * * * * * * * * * | 1 0 1 0 0 0 1 0 0 0 0 | 1 0 1 1 0 ... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 12 * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 ... ... xo.&#x | 2 1 0 | 1 2 0 0 0 0 | * * 6 * * * * * * * * | 0 0 2 0 1 0 0 0 0 0 0 | 1 0 2 0 0 ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * 12 * * * * * * * | 0 0 0 2 1 0 0 0 0 0 0 | 0 1 2 0 0 ... o.x ...&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 12 * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 ... ... x.o&#x | 2 0 1 | 1 0 2 0 0 0 | * * * * * 6 * * * * * | 0 0 0 0 1 0 2 0 0 0 0 | 0 0 2 1 0 .o.3.x. ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 4 * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 ... .x.3.o. | 0 3 0 | 0 0 0 3 0 0 | * * * * * * * 4 * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 ... .xx ...&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * * 12 * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 ..o3..x ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * 4 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 ... ..x3..o | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ---------------+-------+-----------------+---------------------------+------------------------+---------- o..3o..3x.. ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 0 0 1 0 oo.3ox. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 0 0 0 1 0 0 0 0 | * 4 * * * * * * * * * | 1 1 0 0 0 ... ox.3xo.&#x ♦ 3 3 0 | 3 6 0 3 0 0 | 1 3 3 0 0 0 0 1 0 0 0 | * * 4 * * * * * * * * | 1 0 1 0 0 ... oxx ...&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 1 0 2 1 0 0 0 1 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0 ... ... xoo&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 0 1 2 0 1 0 0 0 0 0 | * * * * 6 * * * * * * | 0 0 2 0 0 o.o3o.x ...&#x ♦ 1 0 3 | 0 0 3 0 0 3 | 0 0 0 0 3 0 0 0 0 1 0 | * * * * * 4 * * * * * | 0 1 0 1 0 ... o.x3x.o&#x ♦ 3 0 3 | 3 0 6 0 0 3 | 1 0 0 0 3 3 0 0 0 0 1 | * * * * * * 4 * * * * | 0 0 1 1 0 .o.3.x.3.o. ♦ 0 6 0 | 0 0 0 12 0 0 | 0 0 0 0 0 0 4 4 0 0 0 | * * * * * * * 1 * * * | 1 0 0 0 1 .oo3.xx ...&#x ♦ 0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 0 1 0 3 1 0 | * * * * * * * * 4 * * | 0 1 0 0 1 ... .xx3.oo&#x ♦ 0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 0 0 1 3 0 1 | * * * * * * * * * 4 * | 0 0 1 0 1 ..o3..x3..o ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * 1 | 0 0 0 1 1 ---------------+-------+-----------------+---------------------------+------------------------+---------- oo.3ox.3xo.&#x ♦ 4 6 0 | 6 12 0 12 0 0 | 4 12 6 0 0 0 4 4 0 0 0 | 1 4 4 0 0 0 0 1 0 0 0 | 1 * * * * ooo3oxx ...&#x ♦ 1 3 3 | 0 3 3 3 3 3 | 0 3 0 3 3 0 1 0 3 1 0 | 0 1 0 3 0 1 0 0 1 0 0 | * 4 * * * ... oxx3xoo&#x ♦ 3 3 3 | 3 6 6 3 3 3 | 1 3 3 6 3 3 0 1 3 0 1 | 0 0 1 3 3 0 1 0 0 1 0 | * * 4 * * o.o3o.x3x.o&#x ♦ 4 0 6 | 6 0 12 0 0 12 | 4 0 0 0 12 6 0 0 0 4 4 | 1 0 0 0 0 4 4 0 0 0 1 | * * * 1 * .oo3.xx3.oo&#x ♦ 0 6 6 | 0 0 0 12 6 12 | 0 0 0 0 0 0 4 4 12 4 4 | 0 0 0 0 0 0 0 1 4 4 1 | * * * * 1
o3x3o || oo3ox3xo&#x → height = sqrt(3/5) = 0.774597 (oct || rap) o3o3o .. .. .. | 6 * * | 4 2 1 0 0 0 | 2 2 1 4 2 4 0 0 0 0 0 | 1 2 2 4 1 2 2 0 0 0 0 | 1 2 2 1 0 . . . o.3o.3o. | * 4 * | 0 3 0 3 3 0 | 0 0 3 3 3 0 3 3 3 0 0 | 0 1 3 3 3 0 0 1 1 3 0 | 1 1 3 0 1 . . . .o3.o3.o | * * 6 | 0 0 1 0 2 4 | 0 0 0 0 2 4 0 4 1 2 2 | 0 0 0 4 1 2 2 0 2 2 1 | 0 2 2 1 1 --------------------+-------+-----------------+---------------------------+------------------------+---------- . x . .. .. .. | 2 0 0 | 12 * * * * * | 1 1 0 1 0 1 0 0 0 0 0 | 1 1 1 1 0 1 1 0 0 0 0 | 1 1 1 1 0 o3o3o || o.3o.3o. | 1 1 0 | * 12 * * * * | 0 0 1 2 1 0 0 0 0 0 0 | 0 1 2 2 1 0 0 0 0 0 0 | 1 1 2 0 0 o3o3o || .o3.o3.o | 1 0 1 | * * 6 * * * | 0 0 0 0 2 4 0 0 0 0 0 | 0 0 0 4 1 2 2 0 0 0 0 | 0 2 2 1 0 . . . .. .. x. | 0 2 0 | * * * 6 * * | 0 0 1 0 0 0 2 0 1 0 0 | 0 0 2 0 1 0 0 1 0 2 0 | 1 0 2 0 1 . . . oo3oo3oo&#x | 0 1 1 | * * * * 12 * | 0 0 0 0 1 0 0 2 1 0 0 | 0 0 0 2 1 0 0 0 1 2 0 | 0 1 2 0 1 . . . .. .x .. | 0 0 2 | * * * * * 12 | 0 0 0 0 0 1 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 --------------------+-------+-----------------+---------------------------+------------------------+---------- o3x . .. .. .. | 3 0 0 | 3 0 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 0 0 1 0 0 0 0 0 | 1 1 0 1 0 . x3o .. .. .. | 3 0 0 | 3 0 0 0 0 0 | * 4 * * * * * * * * * | 1 0 1 0 0 0 1 0 0 0 0 | 1 0 1 1 0 o3o3o || .. .. x. | 1 2 0 | 0 2 0 1 0 0 | * * 6 * * * * * * * * | 0 0 2 0 1 0 0 0 0 0 0 | 1 0 2 0 0 . x . || o.3o.3o. | 2 1 0 | 1 2 0 0 0 0 | * * * 12 * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 o3o3o || oo3oo3oo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * 12 * * * * * * | 0 0 0 2 1 0 0 0 0 0 0 | 0 1 2 0 0 . x . || .. .x .. | 2 0 2 | 1 0 2 0 0 1 | * * * * * 12 * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . . . .. o.3x. | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 4 * * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 . . . .. ox ..&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * 12 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . . .. .. xo&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * * * 6 * * | 0 0 0 0 1 0 0 0 0 2 0 | 0 0 2 0 1 . . . .o3.x .. | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * 4 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . .. .x3.o | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 --------------------+-------+-----------------+---------------------------+------------------------+---------- o3x3o .. .. .. ♦ 6 0 0 | 12 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 0 0 1 0 o3x . || o.3o. .. ♦ 3 1 0 | 3 3 0 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 | * 4 * * * * * * * * * | 1 1 0 0 0 . x3o || .. o.3x. ♦ 3 3 0 | 3 6 0 3 0 0 | 0 1 3 3 0 0 1 0 0 0 0 | * * 4 * * * * * * * * | 1 0 1 0 0 . x . || .. ox ..&#x ♦ 2 1 2 | 1 2 2 0 2 1 | 0 0 0 1 2 1 0 1 0 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0 o3o3o || .. .. xo&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 0 1 0 2 0 0 0 1 0 0 | * * * * 6 * * * * * * | 0 0 2 0 0 o3x . || .o3.x .. ♦ 3 0 3 | 3 0 3 0 0 3 | 1 0 0 0 0 3 0 0 0 1 0 | * * * * * 4 * * * * * | 0 1 0 1 0 . x3o || .. .x3.o ♦ 3 0 3 | 3 0 3 0 0 3 | 0 1 0 0 0 3 0 0 0 0 1 | * * * * * * 4 * * * * | 0 0 1 1 0 . . . o.3o.3x. ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 0 4 0 0 0 0 | * * * * * * * 1 * * * | 1 0 0 0 1 . . . oo3ox ..&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 3 0 1 0 | * * * * * * * * 4 * * | 0 1 0 0 1 . . . .. ox3xo&#x ♦ 0 3 3 | 0 0 0 3 6 3 | 0 0 0 0 0 0 1 3 3 0 1 | * * * * * * * * * 4 * | 0 0 1 0 1 . . . .o3.x3.o ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * 1 | 0 0 0 1 1 --------------------+-------+-----------------+---------------------------+------------------------+---------- o3x3o || o.3o.3x. ♦ 6 4 0 | 12 12 0 6 0 0 | 4 4 6 12 0 0 4 0 0 0 0 | 1 4 4 0 0 0 0 1 0 0 0 | 1 * * * * o3x . || oo3ox ..&#x ♦ 3 1 3 | 3 3 3 0 3 3 | 1 0 0 3 3 3 0 3 0 1 0 | 0 1 0 3 0 1 0 0 1 0 0 | * 4 * * * . x3o || .. ox3xo&#x ♦ 3 3 3 | 3 6 3 3 6 3 | 0 1 3 3 6 3 1 3 3 0 1 | 0 0 1 3 3 0 1 0 0 1 0 | * * 4 * * o3x3o || o.3.x3.o ♦ 6 0 6 | 12 0 6 0 0 12 | 4 4 0 0 0 12 0 0 0 4 4 | 1 0 0 0 0 4 4 0 0 0 1 | * * * 1 * . . . oo3ox3xo&#x ♦ 0 4 6 | 0 0 0 6 12 12 | 0 0 0 0 0 0 4 12 6 4 4 | 0 0 0 0 0 0 0 1 4 4 1 | * * * * 1
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