Infinity is a very cute puzzle which uses the symmetry of the five dimensional
structure of the 5-simplex. It is similar to the Pegasus puzzle I did last time,
but now it is edges which are colored, and this gives a meaningful goal to this puzzle.
When minimizing all external rods, the puzzle takes the shape of a solid with a
square base and six triangular faces (Heptahedron). In any case, after making
an extensive search, I had the need to categorise the series of solids which have
a square/rhombus base and the two opposite vertices have a set of new vertices
which are placed at the top and belong to the same "arc" which creates a circle
vertical to the line formed by the other two opposite vertices of the base. Let's call
them as Pantahedron-n
(where n is total number of vertices). For example,
in this case we have six vertices, so it is a Pantahedron-6. Pantahedron-4 is the well
known Tetrahedron (not included in the image).
Pantahedrons.jpg [ 22.66 KiB | Viewed 929 times ]
This type of shape is very common when it comes to Higher Dimensional symmetry (HDs)
structures using telescopic rods and are based on the Complete Graphs Kn, but no specific
name had been given to this category (instead each of those shapes belong individually to
other differently named series).
The goal is to create in the middle the infinity symbol using a specific color.
Infinity_yellow_01.jpg [ 161.81 KiB | Viewed 929 times ]
Solved position with the yellow infinity symbol.
Infinity_red_01.jpg [ 165.79 KiB | Viewed 929 times ]
Solved position with the red infinity symbol.
As a puzzle, Infinity is quite challenging, as unlike Chronos, it requires more than one types
of moves (some are combined, like in the Houlis Cube) to go through its 36 states (72 if we
don't count the trivial ones). And going from one state to another requires a few elongating
and contracting Inside-Out-Turning (IOT) moves.