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'Triangles to Tetrahedra' printed from http://nrich.maths.org/

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What is a tetrahedron? Here are four different triangles made from Polydron (plastic shapes which click together):

 

small equilateral triangle

Small equilateral



Isosceles
right angled triangle

Right angled isosceles
large equilateral triangle

Large equilateral

The sides of the small equilateral triangle are the same length as the short side of the isosceles triangle and the short sides of the right-angled isosceles triangle.

The sides of the large equilateral triangle are the same length as the long sides of the isosceles triangle and the long side of the right-angled isosceles triangle.

You have an unlimited number of each type of triangle.

How many different tetrahedra can you make? Convince us you have found them all.

Images reproduced with kind permission from Polydron International Limited .