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
uniform relative:
bril  
general polytopal classes:
segmentopeta   lace simplices  

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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