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 Post subject: Non-Dodecahedral Starminxes.
PostPosted: Mon Dec 23, 2013 11:46 am 
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Sorry if the thread title is a bit misleading. I am not asking about shapemods of the Starminxes, but rather applying their visually appealing cut patterns to other solids.

I find the Pentagram inscribed within a pentagon cut pattern of the Starminxes to be quite beautiful, and I got to wondering if such patterns can be made on other solids.

The obvious(at least to me) first step is to ask if there is a way of slicing the Truncated Icosahedron such that the pentagons have the same pattern as the Starminx, and the Hexagons are inscribed with a hexagram whose points lie at the corners of the hexagons instead of the edge midpoints. In other words, is there a puzzle that visually is to the Tuttminx what the Starminx is to the Megaminx? Are their multiple ways of slicing the truncated Icosahedron to create such a pattern just as there are (at least) 4 ways of slice the dodecahedron to create the Starminx pattern?

In general, are there any among the Archimedian and Johnson solids that can be slice such that all faces with five or more edges are inscribed with a suitable star polygon(or star figure in the case of Hexagons)?

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 Post subject: Re: Non-Dodecahedral Starminxes.
PostPosted: Mon Dec 23, 2013 12:28 pm 
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I was aking me the same about puzzles with a 6 pointed star, in my collection I have a lot of puzzles with a 5 pointed star but with 6 only four puzzles: dayan gem 3, 4 ,7 and axis cube!
I would like to see if its posible a cubic puzzle wich pattern in a 6 pointed star if it's possible a symetrical one!

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Last edited by Elias Acrich on Mon Dec 23, 2013 1:01 pm, edited 1 time in total.

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 Post subject: Re: Non-Dodecahedral Starminxes.
PostPosted: Mon Dec 23, 2013 12:50 pm 
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If you are only allowing face turns, then no. You could get a pentagram on the pentagonal faces. However, due to the geometry there is now way to create a perfect hexagram (the cuts will instead intersect at the center of the faces, rather than at the corners).
But, if you allow vertex turns...then yes it is possible!
Attachment:
tuttstar.jpg
tuttstar.jpg [ 132.13 KiB | Viewed 587 times ]

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 Post subject: Re: Non-Dodecahedral Starminxes.
PostPosted: Mon Dec 23, 2013 8:25 pm 
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benpuzzles wrote:
Attachment:
tuttstar.jpg


This will need fudging.


So will this.

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 Post subject: Re: Non-Dodecahedral Starminxes.
PostPosted: Tue Dec 24, 2013 12:06 am 
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There's always Adam's Star Puck:
http://www.twistypuzzles.com/cgi-bin/pu ... ?pkey=2935

And I know you are speaking of five pointed stars, but I have to point out something I consider a member of the starminx family of missing corners-- the icosahedral starminx:
http://twistypuzzles.com/forum/viewtopi ... 15&t=26266

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 Post subject: Re: Non-Dodecahedral Starminxes.
PostPosted: Tue Dec 24, 2013 8:10 am 
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So, if I understand correctly:

The FTTI most closely related to the face turning Starminx has the Pentagrams, but simply divides the Hexagons into six triangles. Part of me was thinking that fudging to allow 60 degree Hexagon turns might require adding the hexagrams, but thinking about it more, I thinking such fudging might introduce more weirdness for lack of a better term.

The VTTI most closely related to the Dino Dodecahedron has both the pentagrams and hexagrams, but requires fudging that would likely distort the stars to allow anything other than 360 degree rotations.

The ETTI most closely related to the Edge Turning Starminx would look like the above FTTI if only Hexagon-Hexagon edges turn. The Hexagrams could be added by turns on the Pentagon-Hexgon edges, but such edge turns would be jumble only if possible and might require fudging to make possible.

If the abov VTTI could be made, do you think the same could be done with the Truncated Octahedron and Truncated Tetrahedron, or do you think the asymmetry of their vertexes would be too extreme to fudge?

I think the right combination of edge turns about Octogon-Octogon edges and face turns about Triangles could inscribe Octograms within the octogon faces of the truncated cube, and I think similar can be done with the truncated Dodecahedron. I think the Truncated Cube would be a combination of a Master Skewb and a shallower version of the Helicopter cube, and I am not sure what the truncated Dedecahedron would be(or if the corresponding vertex turning dodecahedron has even been made). Thinking about it more, Compy Cube cuts might also work for inscribing the Octograms on the Truncated cube.

Hmm, if you took a Compy+Shallow Heli or Master Skewb + Shallow Heli, applied it to a truncated Cuboctahedron, adjusted the cut depths to put Octagrams in the Octagons, what would the cut patterns on the squares and Hexgons look like?

I can think of two ways of inscribing Pentagrams in the faces of an Icosidodecahedron, one's a simple Megaminx shape mod, the other turns about the triangular faces with three adjacent triangles being moved along with each turn.

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 Post subject: Re: Non-Dodecahedral Starminxes.
PostPosted: Tue Dec 24, 2013 8:52 am 
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Don't forget the Vertex turning truncated triakis tetrahedron!

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 Post subject: Re: Non-Dodecahedral Starminxes.
PostPosted: Tue Dec 24, 2013 1:07 pm 
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^The Truncated Tetrakis Tetrahedron is quite interesting, not only because it can be sliced in a way that puts a star on every face, but because its what I have dubbed a polydronic Johnson near-miss(that is, an irregularly faced convex solid whose faces are close enough to regular to be constructed with Polydron's regular polygon tiles), and is the rare example of such a shape being considered for a twisty puzzle. Since I can't seem to find any further information on the TTT, could someone tell me what deformation from regular it's faces have?

Also, I think there might a quite a few variants for a flat puzzle based on a hexagonal grid with hexagons with hexagrams in them. Figuring out how to make a flat twisty without curves physical might be a challenge though and having the playing field wrap around(i.e. if a piece moves of one edge, it reappears on the opposite side) might be limited to the realm of simulators.

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