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 Post subject: What do these puzzle have in common? Which are missing?
PostPosted: Mon Nov 09, 2009 12:39 pm 
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See the questions in the subject line.

I made this picture yesterday after finishing the second variant from the bottom right.
Explanation: I wanted a project for learning casting and ended up with this. Ridiculous, I know. :oops:


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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Mon Nov 09, 2009 8:47 pm 
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they're all 3x3 mods!!!
the 3x3 hex dip is missing along with the axis cube

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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Mon Nov 09, 2009 8:52 pm 
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they are all cut on the same axis(the corners), the only thing that changes is how many corners it is cut on......at least that is my guess

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Last edited by Bigandrewgold on Mon Nov 09, 2009 9:08 pm, edited 1 time in total.

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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Mon Nov 09, 2009 8:54 pm 
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They're all corner-truncated 3x3's. Missing all the regular/symmetric mods like the cuboctohedron or whatever it's called? :?

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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Mon Nov 09, 2009 9:05 pm 
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the bottom right one is a cuboctahedron...

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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Mon Nov 09, 2009 10:59 pm 
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They represent a sequence of corner truncations, starting from zero in the upper left, to all eight in the lower right.
From the upper left, you're showing the one cube having one truncated corner, then 2 having 2 truncated corners - you've shown the variants with truncations at diagonally opposing corners on opposite faces, and with adjacent truncations on the same face. You're missing the variant with diagonally opposing truncations on the same face. In general, to be complete, you've got to explore adjacencies on the same face, and opposing truncs on both the same and opposite faces.
Your series proceeds with 3 truncs, 4, 5, 6, the one 7 and the one 8.

You can make all of these variants with the truncated trajber's edge piece, and the half-trunc edge piece.
And the triangle corner.

A nice exercise!

Sorry, I haven't bothered to figure out which others are missing... :wink:

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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Tue Nov 10, 2009 10:53 am 
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Rob is right.

Missing are 8 variants:
One with 2 / 6 truncated corners.
Two with 3 / 5 truncated corners.
Two with 4 truncated corners.

Have I mentioned that I like series of similar mods and don't care about abstractness?


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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Tue Nov 10, 2009 10:58 am 
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Andreas Nortmann wrote:
Have I mentioned that I like series of similar mods and don't care about abstractness?

Good, because we need someone to create a complete puzzle classification system... :wink:

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 Post subject: Re: What do these puzzle have in common? Which are missing?
PostPosted: Tue Nov 10, 2009 1:09 pm 
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Kelvin Stott wrote:
Andreas Nortmann wrote:
Have I mentioned that I like series of similar mods and don't care about abstractness?

Good, because we need someone to create a complete puzzle classification system... :wink:

Which we're trying to do here. :-)


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