Acronym tau tope
Name tetra-augmented tope
Dihedral angles
  • at {4} between hip and squippy:   arccos[-(1+sqrt(40))/sqrt(54)] = 175.376378°
  • at {4} between cube and trip:   arccos[-(2+sqrt(10))/sqrt(27)] = 173.454075°
  • at {3} between toe and tricu:   arccos[-sqrt(5/8)] = 142.238756°
  • at {3} between squippy and trip:   arccos(-sqrt[3/8]) = 127.761244°
  • at {4} between cube and hip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {4} between tricu and trip:   arccos(-1/sqrt(6)) = 114.094843°
  • at {3} between squippy and tricu:   arccos(-1/4) = 104.477512°
  • at {4} between cube and toe:   90°
  • at {6} between hip and toe:   90°
  • at {3} between tricu and tricu:   arccos(1/4) = 75.522488°
Confer
blend-component:
tope   tripuf  
general polytopal classes:
bistratic lace towers  

For this polychoron every alternate hip of tope will be augmented accordingly.


Incidence matrix according to Dynkin symbol

xb3xo3xx xo&#zx   → height = 0, where b = (5+sqrt(10))/3 = 2.720759
(tegum sum of tope and (b,x)-co

o.3o.3o. o.    | 48  * |  1  1  1  1  1  0 | 1  1  1 1  1  1  1  1  1 0 | 1 1 1 1  1  1
.o3.o3.o .o    |  * 12 |  0  0  0  0  4  2 | 0  0  0 0  0  0  2  4  2 1 | 0 0 0 2  1  2
---------------+-------+-------------------+----------------------------+--------------
x. .. .. ..    |  2  0 | 24  *  *  *  *  * | 1  1  1 0  0  0  0  0  0 0 | 1 1 1 0  0  0
.. x. .. ..    |  2  0 |  * 24  *  *  *  * | 1  0  0 1  1  0  1  0  0 0 | 1 1 0 1  1  0
.. .. x. ..    |  2  0 |  *  * 24  *  *  * | 0  1  0 1  0  1  0  1  0 0 | 1 0 1 1  0  1
.. .. .. x.    |  2  0 |  *  *  * 24  *  * | 0  0  1 0  1  1  0  0  1 0 | 0 1 1 0  1  1
oo3oo3oo oo&#x |  1  1 |  *  *  *  * 48  * | 0  0  0 0  0  0  1  1  1 0 | 0 0 0 1  1  1
.. .. .x ..    |  0  2 |  *  *  *  *  * 12 | 0  0  0 0  0  0  0  2  0 1 | 0 0 0 2  0  1
---------------+-------+-------------------+----------------------------+--------------
x.3x. .. ..    |  6  0 |  3  3  0  0  0  0 | 8  *  * *  *  *  *  *  * * | 1 1 0 0  0  0
x. .. x. ..    |  4  0 |  2  0  2  0  0  0 | * 12  * *  *  *  *  *  * * | 1 0 1 0  0  0
x. .. .. x.    |  4  0 |  2  0  0  2  0  0 | *  * 12 *  *  *  *  *  * * | 0 1 1 0  0  0
.. x.3x. ..    |  6  0 |  0  3  3  0  0  0 | *  *  * 8  *  *  *  *  * * | 1 0 0 1  0  0
.. x. .. x.    |  4  0 |  0  2  0  2  0  0 | *  *  * * 12  *  *  *  * * | 0 1 0 0  1  0
.. .. x. x.    |  4  0 |  0  0  2  2  0  0 | *  *  * *  * 12  *  *  * * | 0 0 1 0  0  1
.. xo .. ..&#x |  2  1 |  0  1  0  0  2  0 | *  *  * *  *  * 24  *  * * | 0 0 0 1  1  0
.. .. xx ..&#x |  2  2 |  0  0  1  0  2  1 | *  *  * *  *  *  * 24  * * | 0 0 0 1  0  1
.. .. .. xo&#x |  2  1 |  0  0  0  1  2  0 | *  *  * *  *  *  *  * 24 * | 0 0 0 0  1  1
.. .o3.x ..    |  0  4 |  0  0  0  0  0  4 | *  *  * *  *  *  *  *  * 4 | 0 0 0 2  0  0
---------------+-------+-------------------+----------------------------+--------------
x.3x.3x. ..     24  0 | 12 12 12  0  0  0 | 4  6  0 4  0  0  0  0  0 0 | 2 * * *  *  *
x.3x. .. x.     12  0 |  6  6  0  6  0  0 | 2  0  3 0  3  0  0  0  0 0 | * 4 * *  *  *
x. .. x. x.      8  0 |  4  0  4  4  0  0 | 0  2  2 0  0  2  0  0  0 0 | * * 6 *  *  *
.. xo3xx ..&#x   6  3 |  0  3  3  0  6  3 | 0  0  0 1  0  0  3  3  0 1 | * * * 8  *  *
.. xo .. xo&#x   4  1 |  0  2  0  2  4  0 | 0  0  0 0  1  0  2  0  2 0 | * * * * 12  *
.. .. xx xo&#x   4  2 |  0  0  2  2  4  1 | 0  0  0 0  0  1  0  2  2 0 | * * * *  * 12

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