This is a puzzle based on the six-dimensional symmetry of the Heptapeton, also known as 6-simplex.
The structure is a Pantahedron-7 as seen below.



The solid black lines show the visible (from our point of view) external edges, the solid yellow lines
show the rest of the external edges, and the dotted lines represent the internal edges.

Its structure has two types of rods, those which are external and those which are internal.
When minimising the external rods, it has the shape of a "boat" (Pantahedron-7), while the
internal rods form a star. Using the same shape, there are fourteen different states which
are colored differently. The goal is to create a star which is completely yellow or red. There
is also a challenge of creating a green pentagon.



A yellow star is caged....




A red star is caged...




And here is a green pentagon!

Video here:

http://www.youtube.com/watch?v=vd4jqp3kViM




Pantazis

It reminds me of the impossible box.

I think you're the only person to hold a 'monopoly' of a genre of puzzles for a year.

LOL, this is true, that is, also considering that:

1. There's a patent pending (i.e. a twenty year monopoly by definition anyway!)
with some future plans.

2. The materials are too expensive.

And it is indeed a shape changing impossible-cage! (Now... is all this thing coming closer
to that horrific Tesseract movie, or is it just my idea???)




Pantazis

And in the mean time, Rox still waits on her Farnsworth's cube.

Get on with it bud!

“Rox,” he said, “there is something in there.” His voice now was very steady and yet strange.




Pantazis

PS. A six dimensional Hexeract (which has 64 vertices and valency equal to six) is actually on the works,
but I cannot see it being ready before I leave... In the little story, it says Pentaract, which is wrong spelling
(it is Penteract). Moreover, a Penteract (which would require a rather cumbersome structure based on
valency equal to five - just like the Infinity puzzle) has 32 vertices, not 64.

That is very cool. Possibly my favourite of these 4D puzzles. I do hope I can play with this beast shortly!

It is a lovely puzzle indeed. In fact, this object actually demonstrates that its class
of structures *are* puzzles, as it is not trivial at all to go through different states!
(I had to do a combination of algebraic paper work and regular practice to get
that video right!)

Also, it seems, that I *will* be coming to London, but I won't be able to make it south,
because I will be there for only a couple of days (1st and 2nd of August). Any chance
you could travel to the capital?




Pantazis

I could if I was in England... I'm on holiday at that point.

No you are not. That is, if I capture you inside the Asterius 6D symmetry cage!
(where are you going anyway?)




Pantazis

I'll be in France. Say the UK competition was voted to be in August, I would have got back from France, then gone to the competition for two days, then go back home, have my Birthday, and then fly off to Berlin (If I could go, and if you didn't change the dates). It would be an epic, though very tiring few days.