Posted: Dec 20, 2012 9:26 pm
Microfarad wrote:Using magnetic properties, would be possible to make a unequal-faces fair dice?
One need not use magnetic properties. One may have to adjust the sizes of the faces to get equal probabilities.
But there are some different-face semiregular polyhedra that one can use. The quasi-spherical ones are the Archimedean solids.
Originals:
T: 4(3) ... C: 6(4) ... O: 8(3) ... D: 12(5) .... I: 20(3)
Truncate the vertices:
T: 4(3)+4(6)=8 ... C: 8(3)+6(8) = 14 ... O: 6(4)+8(6)=14 ... D: 20(3)+12(10)=32 ... I: 12(3)+20(6)=32
New vertices of vertex truncations merged:
T: 4(3)+4(3)=8 (regular octahedron) ... C/O: 8(3)+6(4)=14 ... D/I: 20(3)+12(5)=32
Truncate the vertices and edges:
T: 4(6)+4(6)+6(4)=14 (truncated octahedron) ... C/O: 8(6)+6(8)+12(4)=26 ... D/I: 20(6)+12(10)+30(4)=62
New vertices of vertex and edge truncations merged:
T: 4(3)+4(3)+6(4)=14 (vertex-merged truncated cube/octahedron) ... C/O: 8(3)+6(4)+12(4)=26 ... D/I: 20(3)+12(5)+30(4)=62
Snub polyhedra:
T: 4(3)+4(3)+12(3)=20 (regular icosahedron) ... C/O: 8(3)+6(4)+24(3)=38 .... D/I: 20(3)+12(5)+60(3)=92
So one can get sizes 14, 26, 32, 38, 62, 92
Notation: # of (face with # of vertices) + ... = total #