WOLFRAM|DEMONSTRATIONS PROJECT

Tetrahedral and Octahedral Similarohedrons

shape

tetrahedron

octahedron

root

1.32472

This Demonstration shows a tetrahedron or octahedron made with similar but noncongruent triangles. With the tetrahedron, for a given root

r

, two triangles have sides

(

0

r

,

1

r

,

2

r

)

and two have sides

(

1

r

,

2

r

,

3

r

)

. The root is bounded by the golden ratio and its reciprocal:

1/ϕ<r<ϕ

. The octahedron has four of each triangle, with

2

and its reciprocal bounding the root. Edges are labeled with the appropriate power of the root.