Acronym | ... |
Name | rhombic enneacontahedron |
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Vertex figure | [r^{5}], [(r,r')^{3}], [R^{2},R'] |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
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The fatter 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 thinner rhombs {(r',R')^{2}} have vertex angles r' = arccos[sqrt(5)/3] = 41.810315° resp. R' = arccos[-sqrt(5)/3] = 138.189685°.
Esp. r'r' : R'R' = (3+sqrt(5))/2 = 2.618034.
Moreover the second pic above neatly displays the geometry of the 2 types of rhombs in relation to the ike, there being used as vertex representant.
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
abo3oco5ood&#zx → height = 0, a = sqrt(20/3) = 2.581989, b = R'R' = (sqrt(5)-1)/sqrt(3) = 0.713644, c = RR = 2/sqrt(3) = 1.154701, d = r'r' = (1+sqrt(5))/sqrt(3) = 1.868345 o..3o..5o.. | 12 * * | 5 0 | 5 0 [r^{5}] .o.3.o.5.o. | * 60 * | 1 2 | 2 1 [R^{2},R'] ..o3..o5..o | * * 20 | 0 6 | 3 3 [(r,r')^{3}] ----------------+----------+--------+------ oo.3oo.5oo.&#x | 1 1 0 | 60 * | 2 0 .oo3.oo5.oo&#x | 0 1 1 | * 120 | 1 1 ----------------+----------+--------+------ ... oco ...&#xt | 1 2 1 | 2 2 | 60 * {(r,R)^{2}} .bo ... .od&#zx | 0 2 2 | 0 4 | * 30 {(r',R')^{2}}
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