Octahedra Constructed from Eight Identical Triangles

smallest side of triangle

5

middle side of triangle

7

longest side of triangle

8

choose solution

1

2

3

5 7 8

opacity

1

zoom

edge thickness

side color

volume = 96

Eight identical copies of any triangle can be used to construct an octahedron, known as the 4-scalenohedron. Choose an arbitrary integer-sided triangle

T

and the Demonstration builds an octahedron using eight copies of

T

. There are as many as three possible solutions for every set of three sides. Some scalenohedra have rational volumes.

References

[1] Wikipedia. "Bipyramid." (Aug 13, 2015) en.wikipedia.org/wiki/Bipyramid.

External Links

Dipyramid (Wolfram MathWorld)

Scalenohedron

Permanent Citation

Ed Pegg Jr

"Octahedra Constructed from Eight Identical Triangles"
http://demonstrations.wolfram.com/OctahedraConstructedFromEightIdenticalTriangles/
Wolfram Demonstrations Project
Published: August 17, 2015