cayleypy.Puzzles

class cayleypy.Puzzles

Definitions of graphs describing various puzzles.

__init__()

Methods

__init__()
globe_puzzle(a, b)	Cayley graph for Globe puzzle group, a + 1 cycle and 2b order 2 generators.
hungarian_rings(left_size, left_index, ...)	Cayley graph for Hungarian rings puzzle group, generated by rotating two rings in both directions.
megaminx()	Cayley graph for the Megaminx puzzle.
mini_pyramorphix()	Cayley graph for a subgroup of S_24, acting on 24 titles.
pyraminx()	Cayley graph for a subgroup of S_36 acting on 36 tiles.
rubik_cube(cube_size, metric)	Cayley graph for NxNxN Rubik's cube.
starminx()	Cayley graph generated by 20 moves of Starminx puzzle.
starminx_2()	Cayley graph associated with the Starminx 2 puzzle.

static globe_puzzle(a: int, b: int) → CayleyGraphDef

Cayley graph for Globe puzzle group, a + 1 cycle and 2b order 2 generators.

static hungarian_rings(left_size: int, left_index: int, right_size: int, right_index: int) → CayleyGraphDef

Cayley graph for Hungarian rings puzzle group, generated by rotating two rings in both directions.

Parameters:

• left_size –

  • Left ring size.

• left_index –

  • Distance between intersections on the left ring. left_index <= left_size/2

• right_size –

  • Right ring size.

• right_index –

  • Distance between intersections on the right ring. right_index <= right_size/2

static megaminx()

Cayley graph for the Megaminx puzzle.

See https://en.wikipedia.org/wiki/Megaminx.

static mini_pyramorphix() → CayleyGraphDef

Cayley graph for a subgroup of S_24, acting on 24 titles.

It is generated by 17 moves inspired by a simplified version of the Pyramorphix puzzle. Moves are based on overlapping 2- and 3-cycles and result in a symmetric, undirected graph. Order of the graph 24, degree 17, order of the group 288.

static pyraminx() → CayleyGraphDef

Cayley graph for a subgroup of S_36 acting on 36 tiles.

It is generated by 8 elements inspired by Pyraminx puzzle. 4 elements represent rotations of the tetrahedron tips, while 4 others – rotations of its base layers.

static rubik_cube(cube_size: int, metric: str) → CayleyGraphDef

Cayley graph for NxNxN Rubik’s cube.

Parameters:

• cube_size –

  • Size of the cube (N).

• metric –

  • metric defining what counts as one move, one of:

  • ”QSTM” - Quarter Slice Turn Metric.

  • ”QTM” - Quarter Turn Metric.

  • ”HTM” - Half Turn Metric.

  • ”ATM” - Axial Turn Metric.

  • ”fixed_QTM” - fixed left corner with quarter turn moves (support only 2x2x2).

  • ”fixed_HTM” - fixed left corner with half turn moves (support only 2x2x2).

static starminx() → CayleyGraphDef

Cayley graph generated by 20 moves of Starminx puzzle.

Each move is a rotation of a corner, centered around one of the dodecahedron’s pentagonal faces (face centres never move). A single turn corresponds to a set of disjoint 3-cycles, each on one triangular sticker.

static starminx_2() → CayleyGraphDef

Cayley graph associated with the Starminx 2 puzzle.

Generated by 12 moves, corresponding to rotations of the whole dodecahedron’s faces (analogous to face turns in the Megaminx). Unlike the Starminx puzzle, where the generators are vertex-centered, the generators in Starminx 2 are face-centered and affect larger regions of the puzzle.