How to Make a Flat Piece of Paper Into a Sphere by Cutting It Into Geometric Shapes

How does a flat sheet of paper become a hollow sphere? The answer is found in the truncated icosahedron or buckyball, which is a complex arrangement of pentagons and hexagons. While many people may not recognize the term "truncated icosahedron", most will be familiar with an example of this structure: the soccer ball. In the truncated icosahedron, 20 hexagons combine with 12 pentagons to form a flat, two-dimensional pattern. This pattern can then be wrapped around on itself to form a three-dimensional structure that resembles a sphere.

Things You'll Need

  • Card stock
  • Printer
  • Scissors
  • Paper glue
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Instructions

    • 1

      Choose card stock or heavy paper that is compatible with your printer. Copy paper can also be used, but more rigid paper will produce a more sturdy structure.

    • 2

      Print a two-dimensional truncated icosahedron pattern on the card stock.

    • 3

      Cut around the edge of the pattern.

    • 4

      Fold and unfold the pattern along each solid line. Folding will make the structure easier to assemble.

    • 5

      Find two hexagons that are separated by a tab. Apply glue to the top surface of the tab on the one hexagon and tuck the sticky side of the tab under the adjacent hexagon. Press down on the tab to secure it. Repeat for all the neighboring hexagons separated by a tab.

    • 6

      Find a tabbed pentagon that is adjacent to a hexagon. Apply glue to the top surface of the tab on the pentagon and tuck the sticky side of the tab under the adjacent hexagon. Press down on the tab to secure it. Repeat for all the neighboring pentagons and hexagons.

    • 7

      Find any remaining unattached tabs. Apply glue to a tab, and tuck the sticky tab under the nearest neighboring side of a polygon. Continue until all tabs are glued in place and the final structure forms a closed sphere.

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