Two Stellated Rhombic Dodecahedrons
Two Stellated Rhombic Dodecahedrons can be contained in a Cube
In this series of four blog entries, I will be recreating, in the style of, Naoki Yoshimoto's "Shinsei Mystery Puzzles". The word "shinsei" means application in Japanese. This blog entry will explore the puzzle entitled "Yoshimoto's Cube #1". In 1971, Naoki Yoshimoto discovered a way to divide a cube into equal parts in three-dimensional space. The result was a series of three puzzles by Yoshimoto.
"Yoshimoto's Cube #1" is two, twenty four flexible triangular pyramids that are taped together to form a cube or a stellated rhombic dodecahedra depending upon the configuration of the pyramids. Two of these flexible polyhedra can amazingly interlock to form a cube.
After Yoshimoto's discovery of this amazing flexible polyhedra, he introduced it in an exhibit at the Museum of Modern Art entitled "From Cube to Space". In 1982, "Yoshimoto Cube #1" was honored to be included in the museum's permanent collection.
I designed the pyramids to require minimal gluing as there are forty eight pyramids to make. The silver pyramids are smaller than the gold pyramids so that they will fit into the box that I designed to contain the cube. Cut out 24 gold pyramids and assemble them to create the gold stellated rhombic dodecahedron. Repeat for the silver pyramids.
Here is the PDF. I used 65 lb. gold and silver foil cardstock from Michaels.
Here is the .Studio file.
Here is the SVG.
Make the Box
Two of the stellated rhombic dodecahedrons can fit in this box.
Make 24 pyramids in each color, silver and gold.
Cut out 24 pyramids.
Mountain fold all of the dotted lines. Remove the two slits if it did not cut correctly.
Apply glue to the inside of the semicircular tab as shown above.
Insert the tab into the square base. If you have any difficulty inserting the tab, use a needle to widen the slit.
Apply glue to the inside of the other semicircular tab.
Insert the tab into the side of the pyramid.
Completed pyramid.
Assemble the pyramids in groups of three according to color.
Tape two pyramids together at their base. Make sure to cut off any tape that is overhanging the edge of the pyramid.
Tape a third pyramid to this configuration. Make sure to cut off any tape that is overhanging the edge of the pyramid.
Form these three pyramids into a cube shape and tape the edge. Make sure to cut off any tape that is overhanging the edge of the pyramid.
Opposite side of this three pyramid configuration. Continue to make these assemblies until eight has been created.
Complete the assembly of the grouped pyramids into a stellated rhombic dodecahedron
Please note: The tape acts like a hinge and should only be on the surface indicated.
Tape one side of the grouped pyramids together. Repeat for the other three pairs. Make sure to cut off any tape that is overhanging the edge of the pyramid. I turned over one of the pairs on the left so that you could see what the other side looks like.
Place two of the grouped pyramid pairs with the hinges as shown above and...
bring the pairs together to form this star.
Place a third group pair as shown above with its hinge on the top.
Rotate the entire assembly so that the squares are facing you. Apply two strips of tape to the vertical edge where my two fingers are pointing. Make sure to cut off any tape that is overhanging the edge of the pyramid.
Place the last grouped pair with the hinge on the top.
Rotate the entire assembly so that the squares are facing you. Apply two strips of tape to the vertical edge where my two fingers are pointing. Make sure to cut off any tape that is overhanging the edge of the pyramid.
Two Stellated Rhombic Dodecahedrons in a Cube
Two Stellated Rhombic Dodecahedrons can be contained in a Cube
Two Stellated Rhombic Dodecahedrons
and Yoshimoto's Cube #3.
fantastic!
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