m (This construction is also stable without the blue triangles and rods.) |
(Added "Related construction" section, of object with just cubes) |
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Totals given in the summary box. |
Totals given in the summary box. |
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| + | == Related construction == |
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| + | <TABLE border=1 cellpadding=8> |
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| + | <TR><TD>[[Image:Cubes (just) 9725 Med .jpg|400px]] </TD> |
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| + | </TR></TABLE> |
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| + | This object may be constructed by building a rhombicuboctahedron, and then augmenting some of its square faces (specifically those adjacent to triangles) with cubes. Any square face of the rhombicuboctahedron that is surrounded solely by squares should be left as an open hole (in addition to leaving all the triangular faces as open holes). |
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[[Category:Nested Polyhedra]] |
[[Category:Nested Polyhedra]] |
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Revision as of 14:49, 24 January 2010
| Truncated Cuboctahedron of Cubes | |
 Truncated Cuboctahedron of Cubes rendered in Geomag Pastelles | |
| Type | Nested Polyhedra |
| Panels | 24 ×  72 ×  |
| Rods | 168 × 
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| Spheres | 96 × 
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| Author | PolyClare 18:55, 20 January 2010 |
It's a truncated cuboctahedron on the outside, and a rhombicuboctahedron on the inside, and the two are connected by the cubes.
Using this composition, the numbers of rods, spheres, and panels may be quickly counted up:
- 12 pink cubes: 12 x [ 12 pink rods, 6 pink squares, 4 spheres + 4 spheres / shared by 2 cubes ] = 144 rods & 72 squares & 72 spheres
- 24 blue triangles: 24 x [ 1 blue rod , 1 blue triangle, 0 spheres ] = 24 rods & 24 triangles
Totals given in the summary box.
Related construction
The construction described above may be created without the blue triangles and rods. This is actually a stable construction!
 |
This object may be constructed by building a rhombicuboctahedron, and then augmenting some of its square faces (specifically those adjacent to triangles) with cubes. Any square face of the rhombicuboctahedron that is surrounded solely by squares should be left as an open hole (in addition to leaving all the triangular faces as open holes).