Acronym | ... |
Name |
icosahedrally truncated rhombic triacontahedron, chamfered dodecahedron, Goldberg polyhedron GP(2,0) |
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Vertex figure | [5,H^{2}], [h^{3}] |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Confer | rhote doe |
External links |
The non-regular hexahedra {(h,H,H)^{2}} have vertex angles h = arccos(-1/sqrt(5)) = 116.565051° resp. H = arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474°.
Icosahedral truncation applies to the icosahedral vertices (vertex inscribed ike) only. Wrt. the rhote this produces new pentagon faces there. These are then face planes of a cutting doe. – The above transition shows a dynamical mutual scaling of doe and rhote. The chamfered dodecahedron then is the instance, where all edges happen to have the same length.
Chamfering (or edge-only beveling – here being applied to the doe) flatens the former edges into new (non-regular hexagonal) faces.
There is a deeper, terminal chamfering of the doe too, which then reduces the original faces to nothing. Then the hexagons will become rhombs and the total figure becomes the rhote. – When considering the below provided tegum sum Dynkin symbol, it becomes obvious that this figure also can be seen as a Stott expansion of the rhote.
Incidence matrix according to Dynkin symbol
ax5oo3oc&#zx → height = 0 a = 1+sqrt[(10-2 sqrt(5))/5] = 2.051462 c = 2/sqrt(3) = 1.154701 (tegum sum of a-doe and (x,c)-srid) o.5o.3o. | 20 * | 3 0 | 3 0 [h^{3}] .o5.o3.o | * 60 | 1 2 | 2 1 [5,H^{2}] -------------+-------+-------+------ oo5oo3oo&#x | 1 1 | 60 * | 2 0 .x .. .. | 0 2 | * 60 | 1 1 -------------+-------+-------+------ ax .. oc&#zx | 2 4 | 4 2 | 30 * {(h,H,H)^{2}} .x5.o .. | 0 5 | 0 5 | * 12 {5}
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