Acronym redeca
Name rectified decachoron
Net
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Circumradius sqrt(8) = 2.828427
Confer
general polytopal classes:
isogonal  
External
links
hedrondude   polytopewiki  

Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists). Within the specific case of deca all edges belong to a single orbit of symmetry, i.e. rectification clearly is applicable, without any recourse to Conway's ambification (chosing the former edge centers generally). None the less, wrt. the individual cells of the pre-image, there an ambification is possible only, i.e. tut cannot be rectified (within this stronger sense).

Still, because the pre-image uses different polygonal faces, this would result in 2 different edge sizes in the outcome polychoron. That one here is scaled such so that the shorter one becomes unity. Then the larger edge will have size h=sqrt(3).


Incidence matrix according to Dynkin symbol

xo3od3do3ox&#zh   → height = 0
                    d = 3 (pseudo)
(tegum sum of 2 inverted (x,d)-srips)

o.3o.3o.3o.     & | 60 |  2   4 |  1   6  2 |  3  2
------------------+----+--------+-----------+------
x. .. .. ..     & |  2 | 60   * |  1   2  0 |  2  1  x
oo3oo3oo3oo&#h    |  2 |  * 120 |  0   2  1 |  2  1  h
------------------+----+--------+-----------+------
x.3o. .. ..     & |  3 |  3   0 | 20   *  * |  2  0  x-{3}
xo .. .. ..&#h  & |  3 |  1   2 |  * 120  * |  1  1  isot
.. od3do ..&#zh   |  6 |  0   6 |  *   * 20 |  2  0  h-{6}
------------------+----+--------+-----------+------
xo3od3do ..&#zh &  18 | 12  24 |  4  12  4 | 10  *
xo .. .. ox&#h      4 |  2   4 |  0   4  0 |  * 30

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