Acronym respid
Name rectified small prismated decachoron
Net
 ©
Circumradius sqrt(3) = 1.732051
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 spid 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).

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 q=sqrt(2).


Incidence matrix according to Dynkin symbol

uo3ox3xo3ou&#zq   → height = 0
                    u = 2 (pseudo)
(q-laced tegum sum of 2 inverted (u,x)-srips)

o.3o.3o.3o.     | 30  * |  4   4  0 |  2  2  2  2  4  0  0 | 1  1  2  2 0
.o3.o3.o3.o     |  * 30 |  0   4  4 |  0  0  2  4  2  2  2 | 0  2  1  2 1
----------------+-------+-----------+----------------------+-------------
.. .. x. ..     |  2  0 | 60   *  * |  1  1  0  0  1  0  0 | 1  0  1  1 0
oo3oo3oo3oo&#q  |  1  1 |  * 120  * |  0  0  1  1  1  0  0 | 0  1  1  1 0
.. .x .. ..     |  0  2 |  *   * 60 |  0  0  0  1  0  1  1 | 0  1  0  1 1
----------------+-------+-----------+----------------------+-------------
.. o.3x. ..     |  3  0 |  3   0  0 | 20  *  *  *  *  *  * | 1  0  0  1 0  x-{3}
.. .. x.3o.     |  3  0 |  3   0  0 |  * 20  *  *  *  *  * | 1  0  1  0 0  x-{3}
uo .. .. ou&#zq |  2  2 |  0   4  0 |  *  * 30  *  *  *  * | 0  1  1  0 0  q-{4}
.. ox .. ..&#q  |  1  2 |  0   2  1 |  *  *  * 60  *  *  * | 0  1  0  1 0  xqq
.. .. xo ..&#q  |  2  1 |  1   2  0 |  *  *  *  * 60  *  * | 0  0  1  1 0  xqq
.o3.x .. ..     |  0  3 |  0   0  3 |  *  *  *  *  * 20  * | 0  1  0  0 1  x-{3}
.. .x3.o ..     |  0  3 |  0   0  3 |  *  *  *  *  *  * 20 | 0  0  0  1 1  x-{3}
----------------+-------+-----------+----------------------+-------------
.. o.3x.3o.     |  6  0 | 12   0  0 |  4  4  0  0  0  0  0 | 5  *  *  * *  oct
uo3ox .. ou&#zq |  3  6 |  0  12  6 |  0  0  3  6  0  2  0 | * 10  *  * *  retrip
uo .. xo3ou&#zq |  6  3 |  6  12  0 |  0  2  3  0  6  0  0 | *  * 10  * *  retrip
.. ox3xo ..&#q  |  3  3 |  3   6  3 |  1  0  0  3  3  0  1 | *  *  * 20 *  tall (x,q)-3ap
.o3.x3.o ..     |  0  6 |  0   0 12 |  0  0  0  0  0  4  4 | *  *  *  * 5  oct
or
o.3o.3o.3o.     & | 60 |   4   4 |  2  2  2   6 |  1  3  2
------------------+----+---------+--------------+---------
.. .. x. ..     & |  2 | 120   * |  1  1  0   1 |  1  1  1
oo3oo3oo3oo&#q    |  2 |   * 120 |  0  0  1   2 |  0  2  1
------------------+----+---------+--------------+---------
.. o.3x. ..     & |  3 |   3   0 | 40  *  *   * |  1  0  1  x-{3}
.. .. x.3o.     & |  3 |   3   0 |  * 40  *   * |  1  1  0  x-{3}
uo .. .. ou&#zq   |  4 |   0   4 |  *  * 30   * |  0  2  0  q-{4}
.. ox .. ..&#q  & |  3 |   1   2 |  *  *  * 120 |  0  1  1  xqq
------------------+----+---------+--------------+---------
.. o.3x.3o.     & |  6 |  12   0 |  4  4  0   0 | 10  *  *  oct
uo3ox .. ou&#zq & |  9 |   6  12 |  0  2  3   6 |  * 20  *  retrip
.. ox3xo ..&#q    |  6 |   6   6 |  2  0  0   6 |  *  * 20  tall (x,q)-3ap

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