Acronym | choct |
Name |
chamfered octahedron, cubically truncated rhombic dodecahedron |
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Vertex figure | [3,H2], [h4] |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles
(at margins) |
|
Face vector | 30, 48, 20 |
Confer | rad oct |
External links |
The non-regular hexahedra {(h,H,H)2} have vertex angles h = arccos(1/3) = 70.528779° resp. H = arccos[-sqrt(2/3)] = 144.735610°.
Cubical truncation applies to the cubical vertices (vertex inscribed cube) only. Wrt. the rad this produces new triangle faces there. These are then face planes of a cutting oct. – The above transition shows a dynamical mutual scaling of oct and rad. The chamfered oct then is the instance, where all edges happen to have the same length.
Chamfering (or edge-only beveling – here being applied to the oct) flatens the former edges into new (non-regular hexagonal) faces.
There is a deeper, terminal chamfering of the oct too, which then reduces the original faces to nothing. Then the hexagons will become rhombs and the total figure becomes the rad. – 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 rad.
Incidence matrix according to Dynkin symbol
ax3oo4oc&#zx → height = 0 a = (3+2 sqrt(6))/3 = 2.632993 c = 2/sqrt(3) = 1.154701 (tegum sum of a-oct and (x,c)-sirco) o.3o.4o. | 6 * | 4 0 | 4 0 [h4] .o3.o4.o | * 24 | 1 2 | 2 1 [3,H2] -------------+------+-------+----- oo3oo4oo&#x | 1 1 | 24 * | 2 0 .x .. .. | 0 2 | * 24 | 1 1 -------------+------+-------+----- ax .. oc&#zx | 2 4 | 4 2 | 12 * {(h,H,H)2} .x3.o .. | 0 3 | 0 3 | * 8 {3}
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