Thread: Symmetries question

Hi there,

I'm trying to work out the number of symmetries an equilateral triangular prism joined to a tetrahedron at both ends has. I'm seeing 12 symmetries only - can anyone advise me if I am missing out any.

Thanks!

Hello, patrickmustard!

I'm trying to work out the number of symmetries of an equilateral
triangular prism with a regular tetrahedron at both ends.
I'm seeing 12 symmetries only - am I missing out any?

A symmetry would be a plane which divides the solid into two congruent halves.

I find only four of them.
How did you get twelve?

Well by symmetries I mean the identity, rotations, reflections and composites, so apologies if I'm misusing the term. I'm seeing 10 of these 'symmetries' - 6 from the tetrahedron (identity, rotation about 120 and 240 degrees, and 3 reflections), and then a reflection through the vertical plane bisecting the prism and then 3 more rotations about the axes through the midpoint of each prism edge and the centre of the opposite face. I hope you understand what I'm talking about, I'm trying to be as clear as I can! Again the shape I'm talking about is a equilateral triangular prism with a tetrahedron attached to each triangle-shaped end of the prism.