Can you number the vertices, edges and faces of a tetrahedron so
that the number on each edge is the mean of the numbers on the
adjacent vertices and the mean of the numbers on the adjacent
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Right angled isosceles
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.
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