Truncated tetrahedron
A tetrahedron has each corner cut off to produce a solid. What is the total length of the edges of this solid?
Age
11 to 14
Challenge level
Problem
Image
A regular tetrahedron with edges of length 6 cm has each corner cut off to produce the solid shown.
The triangular faces are all equilateral triangles, but not necessarily the same size.
What is the total length of the edges of the resulting solid?
Student Solutions
At each vertex, the piece that has been removed is a regular tetrahedron.
Three of the edges of this are the pieces of edge that are lost from the original tetrahedron, the other three are the new edges of the truncated tetrahedron.
Since all the edges are the same length, the total length of the edges remains unchanged.
Therefore, the total length of the edges is $6\text{cm} \times 6 = 36\text{cm}$.