Acronym | respic |
Name | rectified small prismated tetracontoctachoron |
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Circumradius | sqrt[7+4 sqrt(2)] = 3.557647 |
Coordinates |
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Face vector | 576, 2304, 2112, 384 |
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 spic 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
uo3ox4xo3ou&#zq → height = 0 u = 2 (pseudo) (q-laced tegum sum of 2 inverted (u,x)-sricos) o.3o.4o.3o. | 288 * | 4 4 0 | 2 2 2 2 4 0 0 | 1 1 2 2 0 .o3.o4.o3.o | * 288 | 0 4 4 | 0 0 2 4 2 2 2 | 0 2 1 2 1 ----------------+---------+--------------+-----------------------------+---------------- .. .. x. .. | 2 0 | 576 * * | 1 1 0 0 1 0 0 | 1 0 1 1 0 oo3oo4oo3oo&#q | 1 1 | * 1152 * | 0 0 1 1 1 0 0 | 0 1 1 1 0 .. .x .. .. | 0 2 | * * 576 | 0 0 0 1 0 1 1 | 0 1 0 1 1 ----------------+---------+--------------+-----------------------------+---------------- .. o.4x. .. | 4 0 | 4 0 0 | 144 * * * * * * | 1 0 0 1 0 x-{4} .. .. x.3o. | 3 0 | 3 0 0 | * 192 * * * * * | 1 0 1 0 0 x-{3} uo .. .. ou&#zq | 2 2 | 0 4 0 | * * 288 * * * * | 0 1 1 0 0 q-{4} .. ox .. ..&#q | 1 2 | 0 2 1 | * * * 576 * * * | 0 1 0 1 0 xqq .. .. xo ..&#q | 2 1 | 1 2 0 | * * * * 576 * * | 0 0 1 1 0 xqq .o3.x .. .. | 0 3 | 0 0 3 | * * * * * 192 * | 0 1 0 0 1 x-{3} .. .x4.o .. | 0 4 | 0 0 4 | * * * * * * 144 | 0 0 0 1 1 x-{3} ----------------+---------+--------------+-----------------------------+---------------- .. o.4x.3o. | 12 0 | 24 0 0 | 6 8 0 0 0 0 0 | 24 * * * * co uo3ox .. ou&#zq | 3 6 | 0 12 6 | 0 0 3 6 0 2 0 | * 96 * * * retrip uo .. xo3ou&#zq | 6 3 | 6 12 0 | 0 2 3 0 6 0 0 | * * 96 * * retrip .. ox4xo ..&#q | 4 4 | 4 8 4 | 1 0 0 4 4 0 1 | * * * 144 * tall (x,q)-4ap .o3.x4.o .. | 0 12 | 0 0 24 | 0 0 0 0 0 8 6 | * * * * 24 co
or o.3o.4o.3o. & | 576 | 4 4 | 2 2 2 6 | 1 3 2 ------------------+-----+-----------+------------------+----------- .. .. x. .. & | 2 | 1152 * | 1 1 0 1 | 1 1 1 oo3oo3oo3oo&#q | 2 | * 1152 | 0 0 1 2 | 0 2 1 ------------------+-----+-----------+------------------+----------- .. o.4x. .. & | 4 | 4 0 | 288 * * * | 1 0 1 .. .. x.3o. & | 3 | 3 0 | * 384 * * | 1 1 0 uo .. .. ou&#zq | 4 | 0 4 | * * 288 * | 0 2 0 .. ox .. ..&#q & | 3 | 1 2 | * * * 1152 | 0 1 1 ------------------+-----+-----------+------------------+----------- .. o.4x.3o. & | 12 | 24 0 | 6 8 0 0 | 48 * * co uo3ox .. ou&#zq & | 9 | 6 12 | 0 2 3 6 | * 192 * retrip .. ox4xo ..&#q | 8 | 8 8 | 2 0 0 8 | * * 144 tall (x,q)-4ap
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