Acronym | respid |
Name | rectified small prismated decachoron |
Net |
© © |
Circumradius | sqrt(3) = 1.732051 |
Face vector | 60, 240, 230, 50 |
Confer |
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External links |
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 * * * *red
uo3ox .. ou&#zq ♦ 3 6 | 0 12 6 | 0 0 3 6 0 2 0 | * 10 * * *blue
uo .. xo3ou&#zq ♦ 6 3 | 6 12 0 | 0 2 3 0 6 0 0 | * * 10 * *blue
.. ox3xo ..&#q ♦ 3 3 | 3 6 3 | 1 0 0 3 3 0 1 | * * * 20 *yellow
: verf(spid) .o3.x3.o .. ♦ 0 6 | 0 0 12 | 0 0 0 0 0 4 4 | * * * * 5red
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 * *red
uo3ox .. ou&#zq & ♦ 9 | 6 12 | 0 2 3 6 | * 20 *blue
.. ox3xo ..&#q ♦ 6 | 6 6 | 2 0 0 6 | * * 20yellow
: verf(spid)
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