Triangles to Tetrahedra

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Triangles to Tetrahedra printable sheet

 

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

 

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Triangles to Tetrahedra


Small equilateral
 
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Triangles to Tetrahedra


Isosceles
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Triangles to Tetrahedra


Right angled isosceles
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Triangles to Tetrahedra


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.