GMTRCPLY - GeoMeTRiCPLaY - GeoBender & ShaShiBo

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What are GeoBender and ShaShiBo?

GeoBender and ShaShiBo are enhancements of the "Yoshimoto Cube No.3" by Naoki Yoshimoto.

The structure of the Yoshimoto Cube No.3 is a 12-part Kaleidcycle that folds into a cube shape as its initial state. The elements are face-to-center pyramids cut in half perpendicular along a face diagonal. The resulting elements a scalene tetrahedrons with three different faces. The Kaleidocycle is hinged at adjacent edges, allowing many different shapes from tightly packed to loose structures.

There were many different implementations of the original Yoshimoto Cube No.3 in the 1970s and 1980s, but with moderate success.

The significant enhancement of GeoBender and ShaShiBo is the use of 36 magnets. This does not only keep many of the shapes static, it also allows connecting mutiple units into larger structures.

What is the difference between GeoBender and ShaShiBo?

Physically and mechanically, GeoBender and ShaShiBo are identical. Both use 36 magnets, but the magnetic layout is different. This difference only affects the connections between two or more units, the shapes that are possible with a single unit are not affected.

ShaShiBo use a simplified magnetic layout. This means that most connections between units are easier to achive, because the magnetic orientation of the individual shapes does not matter. On the other hand, certain connections between GeoBender are impossible with ShaShiBo, because of magnetic repel.

The different magnetic layout of GeoBender leads to many shapes that are magnetically chiral. In simplified terms: Many shapes have a magnetic mirror counterpart. If you work with GeoBender combos, you need to know whether the same or the opposite magnetic type will connect. In addition to knowing the transitions between shapes, you also need to know how to turn a shape into its magnetic mirror counterpart.

The Geometry of GeoBender and ShaShiBo

The edge length of the cube shape is 60mm, the AF measurement of the sphere is about 85mm. In geometrical terms, the sphere shape is the inversion of the cube shape, the resulting sold is a Squareroot-2 Rhombic Dodecahedron. The AF measurement is equal to the diameter of the inscribed sphere, equal to a face diagonal of the cube shape.

The dissection creates 12 scalene tetrahedrons with three different types of faces. One face is equal to half of a cube face, another face is the cut of a face-to-center pyramid, the other two faces are lateral faces of a face-to-center pyramd.

Zones and Designs of GeoBender and ShaShiBo

The designs of the 48 triangular facelets of GeoBender and ShaShiBo are usually split in four zones:

• 12 right-angled isosceles triangles making the cube surface,
• 24 isosceles triangles that combine into 12 rhombic faces making the sphere surface,
• 6 thin triangles meeting inside at one vertex of the cube or sphere shape,
• 6 thin triangles meeting inside at the diametrically opposite vertex of the cube or sphere shape.

While the cube and sphere designs can be viewed in the respective shapes, the patterns of the intermediate faces can be best viewed on the two sides of the Star shape.

The "classic" designs were the same across all faces of one zone, and symmetric and continuous across face boundaries when meeting faces from the same zone.

Brand	Design name	Code	Cube design	Intermediate 1	Intermediate 2	Sphere design
GeoBender	Nautilus	GBC-NAUT	Nautilus	Fire	Forest	Water
GeoBender	Primary-I	GBC-PRIM	Solid red	Solid yellow	Solid green	Solid blue
GeoBender	Primary-II	GBC-PRIM2	Solid blue	Solid red	Solid green	Solid yellow
GeoBender	Abstract-I	GBC-ABST	Checkered	Checkered	Lines	Lines
GeoBender	Abstract-II	GBC-ABST2	Rhombic	White with black	Black with white	Black/White
GeoBender	Surfer	GBC-SURF	Emerald	Spume	Fractal	Surfer
GeoBender	Bees	GBC-BEES	Fern	Flowers	Honey	Bees
GeoBender	World	GBC-WORLD	Globe	Waterfall	Lava	Map
GeoBender	Beam	GBC-BEAM	Orange or green	Beams orange	Beams green	Orange and/or green
Brand	Design name	Code	Cube design	Intermediate 1	Intermediate 2	Sphere design
ShaShiBo	Black & White	SHA01BW
ShaShiBo	Blue Planet	SHA02BP
ShaShiBo	Spaced Out	SHA03SO
ShaShiBo	Optical Illusion	SHA04OI
ShaShiBo	Elements	SHA05EM
ShaShiBo	Wings	SHA06WG
ShaShiBo	Moon	SHA07MN
ShaShiBo	Earth	SHA08EA
ShaShiBo	Confetti	SHA09CF
ShaShiBo	Chaos	SHA10CO
ShaShiBo	Mystic Ocean	SHA11MO
ShaShiBo	Undersea	SHA13US
ShaShiBo	Grateful Dead: Skull and Roses	SHA-GDSR
ShaShiBo	Grateful Dead: Dancing Bears	SHA-GDDB
ShaShiBo	Grateful Dead: Steal your Face	SHA-GDSF
ShaShiBo	Grateful Dead: Haight-Ashbury	SHA-GDHA

Some time after the Grateful Dead series, an endless series of new designs startet. As of March 2025, more than 60 different ShaShiBo designs were released.