Hello everyone,
Today I am very pleased to introduce my new twisty puzzle. It is my envision of a higher order Square-1.
Video


I think this is a 4x4 version of the Square-1 for 2 reasons:
1. There are twice as many edge pieces as before (16 instead of 8).
2. There are 4 layers instead of 3.

The puzzle turns like an average Square-1 at first:


However, in reality, the geometry of the puzzle makes it behave differently. Like the original Square-1, two edge pieces together have the same width as one corner piece. But because there are extra edge pieces the geometry of the puzzle is related to an octagonal prism rather than a dodecagonal prism (the original). This can be demonstrated with this position:


Notice that all of the edge pieces are on one layer, and all of the corner pieces are on the other layer (unlike 8 edge, 2 corner on 1 and 6 corner on the other of the original puzzle).

The puzzle also has an extra bonus: instead of there being just one axis for slicing, there are two:

But wait, there's more! Because the puzzle has a deep cut on every axis, it can also shapesift into a 2x2 which can randomly bandage depending on the previous moves:

Here it is scrambled



The puzzle turns VERY well, mainly because I used springs in the core.
This puzzle was inspired by the Brillicube Revenge.

I like it a lot. Those additional possible turns reminds me of Square-1XP. Is the mechanism based on 2x2x2?

And I'm not sure but shouldn't higher order puzzle have more layers on every axis of rotation? In your puzzle you have 4 layers on vertical axis (in standard Square-1 there are 3), but horizontal axis divides it to two halves (as in Square-1) so there are still 2 layers. Could it be possible to add another layer to the puzzle?

Anyway, great puzzle. I'm looking forward to see video.

Krystian

I haven't wanted a puzzle as soon as I saw it in a while. The shape shifting makes this look like too much fun, great job.

What a great idea!
Though I think additional edge split makes it closer to Square-2, but not quite...
Maybe it's a Master Square-1.5?
Vadim

Okay.
The museum knows many variants of the dodecagonal prism and its bandaged cousins. The more exotic puzzles are derived from the decagonal prism, the octadecagonal prism and one radical puzzle which behaves like tetraicosagonal prism.

This is the first bandaged hexadecagonal prism. Cool!

Your images are very good. Thank you for helping in this way.
Can you help me further with edge length and weight?

Andreas

Oh yeah, sorry about that...the size is about 57mmx57mmx62mm. The weight...well, I don't have a scale unfortunately. I'll try to calculate it manually.

...and solved!

This was actually much more difficult than I had originally anticipated. I expected to be able to solve it first like a 2x2 (to return the puzzle to the original form) then by using an edge pairing technique similar to pairing corner pieces on a Square-2, and finally solving it like a Square-1, but it's actually not at all like that. I'll explain more about this later...

***Bump***

Sorry for the bump but I've just added a video (I really need to get on top of these). I will also be auctioning this copy of the puzzle in the near future, so be on the lookout for that as well.
I might be able to put this up for sale on Shapeways, but chances are I won't be able to. We'll see what happens...

This puzzle is just.. wow!