Acronym | ... |
Name | icosa-expanded rhombic enneacontahedron |
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Vertex figure | [r^{5}], [r,h,3,h], [R^{2},H] |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
The rhombs {(r,R)^{2}} have vertex angles r = arccos(1/3) = 70.528779° resp. R = arccos(-1/3) = 109.471221°.
Esp. rr : RR = sqrt(2) = 1.414214.
The hexagons {(h,h,H)^{2}} have vertex angles h = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157° resp. H = arccos[-sqrt(5)/3] = 138.189685°.
This polyhedron is just the Stott expansion of the rhombic enneacontahedron wrt. its icosahedral vertices.
All a, b, c, and d edges, provided in the below description, only qualify as pseudo edges wrt. the full polyhedron.
Incidence matrix according to Dynkin symbol
abx3oco5ood&#zx → height = 0, a = 1+sqrt(20/3) = 3.581989, b = HH = 1+(sqrt(5)-1)/sqrt(3) = 1.713644, c = RR = 2/sqrt(3) = 1.154701, d = hh = (1+sqrt(5))/sqrt(3) = 1.868345 o..3o..5o.. | 12 * * | 5 0 0 | 5 0 0 [r^{5}] .o.3.o.5.o. | * 60 * | 1 2 0 | 2 1 0 [R^{2},H] ..o3..o5..o | * * 60 | 0 2 2 | 1 2 1 [r,h,3,h] ----------------+----------+-----------+--------- oo.3oo.5oo.&#x | 1 1 0 | 60 * * | 2 0 0 .oo3.oo5.oo&#x | 0 1 1 | * 120 * | 1 1 0 ..x ... ... | 0 0 2 | * * 60 | 0 1 1 ----------------+----------+-----------+--------- ... oco ...&#xt | 1 2 1 | 2 2 0 | 60 * * {(r,R)^{2}} .bx ... .od&#zx | 0 2 4 | 0 4 2 | * 30 * {(h,h,H)^{2}} ..x3..o ... | 0 0 3 | 0 0 3 | * * 20
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