Acronym pautpen
Name penta-augmentated truncated pentachoron
Circumradius ...
Dihedral angles
  • at {6} between tricu and tricu:   360°-arccos(-11/16) = 226.567463°
  • at {3} between tet and trip:   arccos(-sqrt[27/32]) = 156.716268°
  • at {3} between oct and trip:   arccos(-sqrt[3/8]) = 127.761244°
  • at {4} between tricu and trip:   arccos(-1/sqrt(6)) = 114.094843°
  • at {3} between oct and tricu:   arccos(-1/4) = 104.477512°
  • at {3} between tricu and tricu:   arccos(1/4) = 75.522488°
Confer
uniform relative:
tip  
segmentochora:
octatut  
blend-components:
octatut   tip  
related CRFs:
autpen  

Note that the A-sized edges would still survive the notational hull operation, but here are assumed to not contribute. Thus the underlying orthogonal hexagons provide non-convex dihedral angles. Nonetheless, this polychoron has the strange property that it's entire surface is exposed, even though it is not convex, that is, it's a non-self-intersecting concave polychoron.


Incidence matrix according to Dynkin symbol

xo3xx3oo3oA&#zx   → height = 0, where A = 3/2

o.3o.3o.3o.    | 20  * |  1  3  3  0 |  3  3  3  6  0  0 | 1  6  3 0
.o3.o3.o3.o    |  * 30 |  0  0  2  4 |  0  0  1  4  2  2 | 0  2  2 1
---------------+-------+-------------+-------------------+----------
x. .. .. ..    |  2  0 | 10  *  *  * |  3  0  3  0  0  0 | 0  6  0 0
.. x. .. ..    |  2  0 |  * 30  *  * |  1  2  0  2  0  0 | 1  2  2 0
oo3oo3oo3oo&#x |  1  1 |  *  * 60  * |  0  0  1  2  0  0 | 0  2  1 0
.. .x .. ..    |  0  2 |  *  *  * 60 |  0  0  0  1  1  1 | 0  1  1 1
---------------+-------+-------------+-------------------+----------
x.3x. .. ..    |  6  0 |  3  3  0  0 | 10  *  *  *  *  * | 0  2  0 0
.. x.3o. ..    |  3  0 |  0  3  0  0 |  * 20  *  *  *  * | 1  0  1 0
xo .. .. ..&#x |  2  1 |  1  0  2  0 |  *  * 30  *  *  * | 0  2  0 0
.. xx .. ..&#x |  2  2 |  0  1  2  1 |  *  *  * 60  *  * | 0  1  1 0
.o3.x .. ..    |  0  3 |  0  0  0  3 |  *  *  *  * 20  * | 0  1  0 1
.. .x3.o ..    |  0  3 |  0  0  0  3 |  *  *  *  *  * 20 | 0  0  1 1
---------------+-------+-------------+-------------------+----------
.. x.3o.3o.      4  0 |  0  6  0  0 |  0  4  0  0  0  0 | 5  *  * *
xo3xx .. ..&#x   6  3 |  3  3  6  3 |  1  0  3  3  1  0 | * 20  * *
.. xx3oo ..&#x   3  3 |  0  3  3  3 |  0  1  0  3  0  1 | *  * 20 *
.o3.x3.o ..      0  6 |  0  0  0 12 |  0  0  0  0  4  4 | *  *  * 5

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