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Exploring Some Geometric Themes

A flat plan that folds up

A cube-shaped box, opened flat, is six squares joined in one piece. Fold the piece back and the box is whole again. The face the box stands on is its base.

A flat net: six squares.
Step 1 of 3
  1. A flat net: six squares.
  2. Fold up the four squares touching the base.
  3. Fold the last square over the top to close it.

Rule: A net is a flat plan that folds into a solid. One flat piece per face. No piece covers another.

On a cube net, every square joins another edge to edge. A cube has 11 different nets. A turned or flipped net is not a new one.

Cuboids, prisms and pyramids have nets too. A tetrahedron has 4 triangle faces. Only 2 ways of joining the triangles fold up. One is a strip of four triangles. The other is one triangle with a triangle on each side.

Slide Fold. Watch the flat plan become a box.

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This track

  1. 0 Start here
  2. 1 Faces, edges and corners
  3. 2 A flat plan that folds up
  4. 3 Six squares, and most plans do not fold
  5. 4 What you see from where
  6. 5 A relation hiding in the counts
  7. 6 A shape inside itself
  8. 7 What each stage really does
  9. 8 The carpet, and fractals around us
  10. 9 The big picture
  11. 10 Track quiz

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