000RM.dvi

1110 Tetrahedra

42.4 Charles Twigg’s envelope model of the tetrahedron

2

Take an sealed envelope which is two copies of a rectangleABCDglued
along the perimeter. AssumeAB < BC.
A

B C

D

E=E′

F

1.Fold the diagonalsACandBD. Their intersection is the double

pointEandE′.

2.Cut along two half diagonalsAE andDEto remove the sector

containing one long side and the flap of the envelope.

3.Fold along the remaining portions of the half diagonals (BEand

CE) and crease firmly. Fold back along the same lines and crease

firmly again.

4.FoldABintoDCto form the creaseEF. Here,Fis the midpoint

of the sideBC. UnderneathEis the pointE′

5.SeparateEandE′untilEFE′is a straight line. Fold up around

EFE′untilDmeetsA, thus forming a hexahedron.

6.TuckDunderAB(orAunderDC) and press up onBandCuntil

DCandBAcoincide.

A=C

B=D E

E′

F

(^2) C. W. Trigg, Tetrahedral models from envelopes,Math. Mag., 51 (1978) 66–67.