Acronym | reco |
Name |
rectified cuboctahedron, variation of small rhombicuboctahedron, Waterman polyhedron number 6 wrt. primitive cubic lattice C3 centered at a lattice point, Waterman polyhedron number 3 wrt. face-centered cubic lattice A3 centered at a lattice point |
© | |
Circumradius | sqrt(3) = 1.732051 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles |
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Face vector | 24, 48, 26 |
Confer |
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Measures are using edge sizes x = 1 and q = sqrt(2) = 1.414214.
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 co 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).
Incidence matrix according to Dynkin symbol
x3o4q . . . | 24 | 2 2 | 1 2 1 ------+----+-------+------- x . . | 2 | 24 * | 1 1 0 . . q | 2 | * 24 | 0 1 1 ------+----+-------+------- x3o . | 3 | 3 0 | 8 * * x . q | 4 | 2 2 | * 12 * . o4q | 4 | 0 4 | * * 6
q4/3o3/2x . . . | 24 | 2 2 | 1 2 1 ----------+----+-------+------- q . . | 2 | 24 * | 1 1 0 . . x | 2 | * 24 | 0 1 1 ----------+----+-------+------- q4/3o . | 4 | 4 0 | 6 * * q . x | 4 | 2 2 | * 12 * . o3/2x | 3 | 0 3 | * * 8
uo3xx3ou&#zq → height = 0 o.3o.3o. | 12 * | 2 2 0 | 1 1 2 0 .o3.o3.o | * 12 | 0 2 2 | 0 1 2 1 -------------+-------+----------+--------- .. x. .. | 2 0 | 12 * * | 1 0 1 0 oo3oo3oo&#q | 1 1 | * 24 * | 0 1 1 0 .. .x .. | 0 2 | * * 12 | 0 0 1 1 -------------+-------+----------+--------- .. x.3o. | 3 0 | 3 0 0 | 4 * * * uo .. ou&#zq | 2 2 | 0 4 0 | * 6 * * .. xx ..&#q | 2 2 | 1 2 1 | * * 12 * .o3.x .. | 0 3 | 0 0 3 | * * * 4
or o.3o.3o. & | 24 | 2 2 | 1 1 2 ---------------+----+-------+------- .. x. .. & | 2 | 24 * | 1 0 1 oo3oo3oo&#q | 2 | * 24 | 0 1 1 ---------------+----+-------+------- .. x.3o. & | 3 | 3 0 | 8 * * uo .. ou&#zq | 4 | 0 4 | * 6 * .. xx ..&#q | 4 | 2 2 | * * 12
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