The Impossiball is a rounded

icosahedral In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...

puzzle similar to the

Rubik's Cube The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...

. It has a total of 20 movable pieces to rearrange, which is the same as the Rubik's Cube, but all of the Impossiball's pieces are corners, like the

Pocket Cube The 2x2 Rubik's Cube (also known as the Pocket Cube or Mini Cube) is a 2×2×2 version of the Rubik's Cube. The cube consists of 8 pieces, all corners. History In March 1970, Larry D. Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in ...

History

William O. Gustafson applied for a patent for the Impossiball design in 1981 and it was issued in 1984.Impossiball patent
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Uwe Mèffert Uwe Mèffert (28 November 1939–30 April 2022) was a German puzzle designer and inventor. He manufactured and sold mechanical puzzles in the style of Rubik's Cube since the Cube craze of the 1980s. His first design was the Pyraminx – which he ...

eventually bought the rights to some of the patents and continues to sell it in his puzzle shop under the Impossiball moniker.

Description

The Impossiball is made in the shape of an

icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...

that has been rounded out to a sphere, and has 20 pieces, all of them corners. The puzzle has twelve circles located at the vertices of the icosahedron, and on the six-color version opposite circles are the same color. Because of the rounded shape of the puzzle, the pieces move up and down as they are rotated. It is also possible to remove one piece, turning the puzzle into a spherical version of the

15 puzzle The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle having 15 square tiles numbered 1–15 in a frame that is 4 tiles high and 4 tiles wide, leaving one unoccupied tile position ...

. The purpose of the puzzle is to scramble the colors, and then restore it to its original state of having one color per circle. This puzzle is equivalent to solving just the corners of a

Megaminx The Megaminx or Mégaminx (, ) is a dodecahedron-shaped puzzle similar to the Rubik's Cube. It has a total of 50 movable pieces to rearrange, compared to the 20 movable pieces of the Rubik's Cube. History The Megaminx, or Magic Dodecahedron, ...

or solving a

Kilominx The Megaminx or Mégaminx (, ) is a dodecahedron-shaped puzzle similar to the Rubik's Cube. It has a total of 50 movable pieces to rearrange, compared to the 20 movable pieces of the Rubik's Cube. History The Megaminx, or Magic Dodecahedron, ...

. The original Impossiball had the same colors as the Rubik's Cube: red, orange, yellow, green, blue, and white. Meffert currently produces two versions, one with six colors and one with twelve. The six-color version (pictured) uses pink, two shades of orange, yellow, green, and blue. All the pieces are still distinguishable, however, because the two pieces with the same three colors are mirror images of each other. The twelve-color version has red, pink, orange, yellow, two shades of green, three shades of blue, purple, brown, and white.

Solutions

The Impossiball is functionally equivalent to the Kilominx, or solving the corners of a Megaminx, just with a spherical shape. Thus, the same solutions on the Kilominx can be used on the Impossiball.

Number of combinations

There are 20!/2 ways to arrange the pieces, since there is no way to create odd permutations without tampering with the puzzle. There are 3¹⁹ ways to orient the pieces, since the orientation of the last depends on that of the preceding ones. Since the Impossiball has no fixed face centers, this result is divided by 60. There are 60 possible positions and orientations of the first corner, but all are equivalent because of the lack of face centers. :

\frac \approx 2.36 \times 10^

The entire number is (roughly 23.6 septillion on the

short scale The long and short scales are two of several naming systems for integer power of 10, powers of ten which use some of the same terms for different magnitudes. For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one m ...

or 23.6 quadrillion on the long scale).

References

External links