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 Post subject: Idea for puzzle - Junior DogicPosted: Sat Jul 28, 2001 8:51 pm

Joined: Sun May 27, 2001 7:03 pm
I dont know whether someone has had this idea before, but here goes...

This puzzle is an octahedron with 4 triangles to each side just like the skewb diamond. But instead of turning the way the skewb diamond does the tips turn and so do four entire adjacent faces (just like on the dogic the tips turn and also 5 adjacent faces). Instead of having the 8 faces coloured, there could be a colouring scheme similar to the dogic with the 6 vertices coloured - the centre triangle of each face would have the three colours of its surrounding vertices and each vertex would be made up of four adjacent triangle pieces each of the same colour.

I guess this would be hard to make, but it would really be like a junior dogic...

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 Post subject: Pics?Posted: Sun Jul 29, 2001 8:55 am

Joined: Wed Nov 24, 1999 12:18 pm
Location: Palerang Shire, NSW, Australia
Can you scan some hand drawings to demonstrate the idea?

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 Post subject: Junior Dogic pic onlinePosted: Sun Jul 29, 2001 8:57 am
I made a crude JPG of what I understood. It uses the classic Rubik's color scheme.

Hope that helps!

Jason

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 Post subject: 4x4x4 cube variationPosted: Sun Jul 29, 2001 4:30 pm

Joined: Thu Dec 16, 1999 9:31 am
Location: Kaunas, Lithuania
You can make it from Rubik's Revenge. Make all the edge cubelets indistinguishable (peeling off the stickers or changing them to ones of neutral gray color) and have fun. If to the simple color variation to add less simple :-))
shape variation, you'll get exactly what you want.

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 Post subject: 4x4x4 not quite the samePosted: Sun Jul 29, 2001 6:05 pm

Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
You cannot quite make it from the 4x4x4 cube. The octahedrons tip triangles do indeed correspond to the cubes centres, but the face traingles do not correspond to the cubes corners but actually to the 8 (non-existent) interior cubies.

Jaap

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 Post subject: Thanks guys - and some more ideasPosted: Mon Jul 30, 2001 3:24 am

Joined: Sun May 27, 2001 7:03 pm
First of all, thanks for all the response. Secondly, your picture was spot on Jason - I should have thought of that and included one in my original message. Lastly, the octahedron is the dual of the cube - the correspondence is: midpoints of the square faces of the cube correspond to corners of the octahedron and corners of the cube correspond to midpoints of the triangular faces of the octahedron. So a simpler way of realising it as a 4x4x4 cube IS to get rid of the edge pieces - the corners of a 4x4x4 cube (which conveniently already have the 3 necessary colours for matching the centre pieces) DO correspond to the centre pieces in the 'junior dogic'. But your way works equally well Jaap (8 invisible cubies inside the cube). This way, you actually get to see them and use them just like in solving the dogic. Well done, Juozas, for realising the connection - I hadnt thought of it!
I guess the connection with the dogic is that after you solve it to a point that the vertex triangles match up with their centre 'indicator' triangles, the puzzle solves like a 2x2x2 cube. In a dogic, once the vertex triangles are matched up, it solves like an impossiball (which is equivalent to a megaminx without edges, and as such, is a dodecahedral version of a 2x2x2 cube). The icosahedron is the dual of a dodecahedron... so I guess this is what you would expect to happen.
If you tried to do something similar with a tetrahedron you would probably have be able to turn the faces by themselves. Does anyone want to turn an Alexander's star into a more advanced dogic?

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 Post subject: copy cat I think, sort ofPosted: Mon Jul 30, 2001 6:30 am

Joined: Sat Apr 22, 2000 2:51 am
Location: New Ulm, Minnesota, USA
Isn't that sort of like a Skewb Diamond? No offence.

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 Post subject: Copycat?Posted: Mon Jul 30, 2001 6:34 am

Joined: Sun Dec 19, 1999 3:02 am
You might think so to look at it, but it's not, really. If I understand the description well enough, you rotate the tips instead... either the "mini tips" or 4 sides at once. Creating such a puzzle is easily doable, and an internal mechanism for it already exists. I'll leave the mechanics involved as an exercise for the reader. L8r.

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 Post subject: Sorry--didn't expect it to auto-load.Posted: Mon Jul 30, 2001 8:57 am
I'll leave it online for a few weeks, anyway.

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 Post subject: octahedral dogicPosted: Mon Jul 30, 2001 12:12 pm

Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
Hi James,

Well, you're not quite the first, as I mention this idea on my puzzle ideas page:

http://www.org2.com/jaap/puzzles/ideas.htm

Still, I'm probably not the first, either.
Jaap

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 Post subject: 4x4x4 is dual of octahedronPosted: Mon Jul 30, 2001 4:19 pm

Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
I still do not believe that the 4x4x4 centres+corners are equivalent to the mini dogic. On such a 4x4x4, the a quarter turn of a face cycles the 4 corners (plus 4 centres). This must correspond to a 4 cycle of face centres on the mini dogic, but such a slice move on the dogic moves 8 other pieces, not 4.

I said that the mini dogic corresponds to the face centres and the interior pieces of the cube, which I still think is true. It is indeed possible to invert this model to get a different correspondence, viz:

Mini dogic face centres correspond to cube corners.
Mini dogic corner triangles correspond to cube EDGES.

So you can make an equivalent puzzle by using 8 colours to colour the 8 2x2x2 subcubes of the 4x4x4 cube, except that the face centres are left blank.

Jaap

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 Post subject: Hmmm...Posted: Tue Jul 31, 2001 6:34 am

Joined: Sun Dec 19, 1999 3:02 am
It appears that people here have already figured it out. D'oh! That'll teach me to respond before reading through the rest of the replies first. :-/ L8r.

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 Post subject: Oops!Posted: Tue Jul 31, 2001 4:19 pm

Joined: Sun May 27, 2001 7:03 pm
Thats right actually Jaap - with the corners, you couldnt rotate just the 4 'tips' (= centres of 4x4x4)without also moving the 'centres' (= corners of 4x4x4)!
So you would have to have invisible cubies inside...

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 Post subject: Let's make it from 2x2x2Posted: Wed Aug 01, 2001 3:53 pm

Joined: Thu Dec 16, 1999 9:31 am
Location: Kaunas, Lithuania
You are right; a 4x4x4 cube isn't a good start point. Actually, trying to imagine a mechanism, I started from Ibrahim K. Abu-Shumays and Mary D. Abu-Shumays extended 2x2x2 cube, depicted in great Joshua Bell webpage http://www.calormen.com/TwistyPuzzles/twisty.htm
Thinking, where to place a tricolor piece equivalent, I choused easy but wrong path. A better way is to shave corners of initial 2x2x2 cube and then extend it, using pieces of appropriate form.
I think, those, who already make puzzles, based on 2x2x2 mechanism, could easily manufacture the Junior Dogic.

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