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I have a 10 sided "cube", which is made by "Wonderful Puzzler" (they also

make crappy cheapo regular cubes). The guts are essentially the same as

the regular cube, but the corners are cut off.

If you look down from the top, you see an octogon. The edges are all the

same as a regular cube, but since the corners are cut, they are one color

(thus the 10 colors). For example, there are red, blue, and orange

faces. On an ordinary cube you would have a red-blue-orange corner cubie,

but on this in its place is a pink face. To make this clearer, here is

the coloring of the thing:

red * light-blue**gold**yellow**blue**pink**orange**violet**green * white

(red on top, white on bottom, looking at the blue face, back face is green,

right face is orange, left face is gold).

The interesting thing about this is that unlike the ordinary cube, every cube

does not have a place, you dont know that the pink corner goes between the

blue and orange faces (in an ordinary cube it is the red-blue-orange corner

so you know where it goes). To solve it, you just put the corners in some

order, solve it using the usual transformations, and then if you get a

"parity error" you must go back to the top layer but switch two of the corners

and solve it again. Thus in general you have to solve it almost 2 times!

(almost because you dont have to redo the top layer or half of the second

layer (this assumes you solve top down, which I do.)).

What I mean by parity error is that if the corners are switched you can get

a configuration that in an ordinary cube would tell you the cube is put

together wrong. For example, you can be solving it and get to a point where

an odd number of edges must be fliped.

There may be a transformation to flip an odd number of edges with this cube,

but I have not found it. Anyway its more interesting to solve and it

changes it shape in general with each transformation. (unlike the cube

which stays a cube; this is a octagonal prism).

Alan

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