Acronym arse aurap
Name around-symmetrically expanded augmented rectified pentachoron
Dihedral angles
  • at {6} between tricu and tricu   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between oct and tet   arccos[-(3 sqrt(5)-1)/8] = 135.522488°
  • at {3} between oct and trip:   arccos[-sqrt(3/8)] = 127.761244°
  • at {3} between tet and tricu:   120°
  • at {4} between co and trip:   arccos[-1/sqrt(6)] = 114.094843°
  • at {4} between tricu and trip:   arccos[-1/sqrt(6)] = 114.094843°
  • at {3} between co and oct:   arccos(-1/4) = 104.477512°
  • at {3} between oct and tricu:   arccos(-1/4) = 104.477512°
  • at {4} between tricu and tricu:   90°
  • at {3} between co and tricu:   arccos(1/4) = 75.522488°
Face vector 28, 84, 80, 24
Confer
related segmentochora:
tetatut   coatut  
related Blind polytope:
aurap  
general polytopal classes:
bistratic lace towers  

Incidence matrix according to Dynkin symbol

oox3oxo3xxx&#xt   → height(1,2) = 1/sqrt(2) = 0.707107
                    height(2,3) = sqrt(5/8) = 0.790569
(tet || pseudo tut || co)

o..3o..3o..     | 4  *  * ♦ 3  3  0 0  0  0  0 | 3  3 3 0 0  0  0  0 0 0 0 | 1 1 3 0 0 0 0
.o.3.o.3.o.     | * 12  * | 0  1  2 1  2  0  0 | 0  2 1 1 2  1  2  2 0 0 0 | 0 1 2 1 1 2 0
..o3..o3..o     | *  * 12 | 0  0  0 0  2  2  2 | 0  0 0 0 0  2  1  2 1 2 1 | 0 0 0 1 2 1 1
----------------+---------+--------------------+---------------------------+--------------
... ... x..     | 2  0  0 | 6  *  * *  *  *  * | 2  0 1 0 0  0  0  0 0 0 0 | 1 0 2 0 0 0 0
oo.3oo.3oo.&#x  | 1  1  0 | * 12  * *  *  *  * | 0  2 1 0 0  0  0  0 0 0 0 | 0 1 2 0 0 0 0
... .x. ...     | 0  2  0 | *  * 12 *  *  *  * | 0  1 0 1 1  0  1  0 0 0 0 | 0 1 1 1 0 1 0
... ... .x.     | 0  2  0 | *  *  * 6  *  *  * | 0  0 1 0 2  0  0  2 0 0 0 | 0 0 2 0 1 2 0
.oo3.oo3.oo&#x  | 0  1  1 | *  *  * * 24  *  * | 0  0 0 0 0  1  1  1 0 0 0 | 0 0 0 1 1 1 0
..x ... ...     | 0  0  2 | *  *  * *  * 12  * | 0  0 0 0 0  1  0  0 1 1 0 | 0 0 0 1 1 0 1
... ... ..x     | 0  0  2 | *  *  * *  *  * 12 | 0  0 0 0 0  0  0  1 0 1 1 | 0 0 0 0 1 1 1
----------------+---------+--------------------+---------------------------+--------------
... o..3x..     | 3  0  0 | 3  0  0 0  0  0  0 | 4  * * * *  *  *  * * * * | 1 0 1 0 0 0 0
... ox. ...&#x  | 1  2  0 | 0  2  1 0  0  0  0 | * 12 * * *  *  *  * * * * | 0 1 1 0 0 0 0
... ... xx.&#x  | 2  2  0 | 1  2  0 1  0  0  0 | *  * 6 * *  *  *  * * * * | 0 0 2 0 0 0 0
.o.3.x. ...     | 0  3  0 | 0  0  3 0  0  0  0 | *  * * 4 *  *  *  * * * * | 0 1 0 1 0 0 0
... .x.3.x.     | 0  6  0 | 0  0  3 3  0  0  0 | *  * * * 4  *  *  * * * * | 0 0 1 0 0 1 0
.ox ... ...&#x  | 0  1  2 | 0  0  0 0  2  1  0 | *  * * * * 12  *  * * * * | 0 0 0 1 1 0 0
... .xo ...&#x  | 0  2  1 | 0  0  1 0  2  0  0 | *  * * * *  * 12  * * * * | 0 0 0 1 0 1 0
... ... .xx&#x  | 0  2  2 | 0  0  0 1  2  0  1 | *  * * * *  *  * 12 * * * | 0 0 0 0 1 1 0
..x3..o ...     | 0  0  3 | 0  0  0 0  0  3  0 | *  * * * *  *  *  * 4 * * | 0 0 0 1 0 0 1
..x ... ..x     | 0  0  4 | 0  0  0 0  0  2  2 | *  * * * *  *  *  * * 6 * | 0 0 0 0 1 0 1
... ..o3..x     | 0  0  3 | 0  0  0 0  0  0  3 | *  * * * *  *  *  * * * 4 | 0 0 0 0 0 1 1
----------------+---------+--------------------+---------------------------+--------------
o..3o..3x..     ♦ 4  0  0 | 6  0  0 0  0  0  0 | 4  0 0 0 0  0  0  0 0 0 0 | 1 * * * * * *
oo.3ox. ...&#x  ♦ 1  3  0 | 0  3  3 0  0  0  0 | 0  3 0 1 0  0  0  0 0 0 0 | * 4 * * * * *
... ox.3xx.&#x  ♦ 3  6  0 | 3  6  3 3  0  0  0 | 1  3 3 0 1  0  0  0 0 0 0 | * * 4 * * * *
.ox3.xo ...&#x  ♦ 0  3  3 | 0  0  3 0  6  3  0 | 0  0 0 1 0  3  3  0 1 0 0 | * * * 4 * * *
.ox ... .xx&#x  ♦ 0  2  4 | 0  0  0 1  4  2  2 | 0  0 0 0 0  2  0  2 0 1 0 | * * * * 6 * *
... .xo3.xx&#x  ♦ 0  6  3 | 0  0  3 3  6  0  3 | 0  0 0 0 1  0  3  3 0 0 1 | * * * * * 4 *
..x3..o3..x     ♦ 0  0 12 | 0  0  0 0  0 12 12 | 0  0 0 0 0  0  0  0 4 6 4 | * * * * * * 1

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