Home >> Science & Nature >> Science

How to Put Together a Trapezohedron

A trapezohedron is a geometric solid made up of an even number of identical four-sided faces. The faces are deltoidal or kite-shaped, and arranged to form a faceted, cone-like shape on either end of the solid. A simple six-sided example is a cube, standing on a corner; another is the 10-sided die commonly used in fantasy role-playing games. Models of trapezohedra are somewhat difficult to design, due to the kite-shaped faces. However, once drawn they are relatively straightforward to put together.

Things You'll Need

Pencil
Paper
Ruler
Scissors
Tape

Instructions

Lay Out Your Figures
- 1
  Draw a deltoid, a kite-shaped figure with two short edges and two long ones, using your ruler. The ratio of the height to the width will determine how "fat" or "skinny" the trapezohedron will be; about a 1-to-2 ratio works well. Measure the sides as you draw, so that you can reproduce it.
- 2
  Draw a second kite of the same size so that it reflects the first and is joined to it along a long edge.
- 3
  Continue to draw deltoids, gradually going around a circle, until you have as many as you wish or until you no longer have room. Draw at least three, while four to six is a workable number.
- 4
  Draw a second array of deltoids identical to the first.
Assemble Your Trapezohedron
- 5
  Cut out both figures carefully along their outer edges.
- 6
  Crease the first figure gently along the edges of each face, until you are able to tape the long edges together to form a faceted cone. Do the same with the other figure.
- 7
  Tape the open edges of the two segments together so that all the edges join.

Science