# Tetrahedral and Octahedral Similarohedrons

Tetrahedral and Octahedral Similarohedrons

This Demonstration shows a tetrahedron or octahedron made with similar but noncongruent triangles. With the tetrahedron, for a given root , two triangles have sides and two have sides . The root is bounded by the golden ratio and its reciprocal: . The octahedron has four of each triangle, with and its reciprocal bounding the root. Edges are labeled with the appropriate power of the root.

r

(,,)

0

r

1

r

2

r

(,,)

1

r

2

r

3

r

1/ϕ<r<ϕ

2