Number of ways to unwrap a polyhedra

Shape and space, angle and circle properties, ...
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elendiastarman
Posts: 410
Joined: Sat Dec 22, 2007 8:15 pm

Number of ways to unwrap a polyhedra

Post by elendiastarman » Tue Feb 02, 2010 11:14 pm

When we unwrap a cube, we usually elect to do it in such a way as to form a cross, like so:

0X0
XXX
0X0
0X0

But, you can also unwrap it in a zig-zag fashion, like so:

XX00
0XX0
00XX
How many ways can you unwrap a cube?
How many ways can you unwrap a cube with the caveat that each face is joined to 2 or fewer other faces?
How many ways can you unwrap an icosahedron?
How many ways can you unwrap an icosahedron with the caveat that each face is joined to 2 or fewer other faces?
Want some
3.14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679...?
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uws8505
Posts: 58
Joined: Tue Sep 30, 2008 2:13 pm
Location: South Korea

Re: Number of ways to unwrap a polyhedra

Post by uws8505 » Fri Feb 05, 2010 7:03 pm

For the cubes(11 total, 4 whose faces are joined to <=2 other faces)
XXX  XX0  XX0  XX0  0X0  0X0  X00  X00  X00  X00
0X0  0XX  0X0  0X0  XX0  XXX  XXX  XX0  XX0  XX0
0X0  0X0  0XX  0X0  0XX  0X0  0X0  0XX  0X0  0XX
0X0  0X0  0X0  0XX  0X0  0X0  0X0  0X0  0XX  00X

XXX00
00XXX
Math and Programming are complements

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