A semiregular Polyhedron whose faces are all Equilateral Triangles. There are an infinite number of deltahedra, but only eight convex ones (Freudenthal and van der Waerden 1947). They have 4, 6, 8, 10, 12, 14, 16, and 20 faces. These are summarized in the table below, and illustrated in the following figures.

Name | |

4 | Tetrahedron |

6 | Triangular Dipyramid |

8 | Octahedron |

10 | Pentagonal Dipyramid |

12 | Snub Disphenoid |

14 | Triaugmented Triangular Prism |

16 | Gyroelongated Square Dipyramid |

20 | Icosahedron |

The Stella Octangula is a concave deltahedron with 24 sides:

Another with 60 faces is a ``caved in'' Dodecahedron which is Icosahedron Stellation .

Cundy (1952) identifies 17 concave deltahedra with two kinds of Vertices.

**References**

Cundy, H. M. ``Deltahedra.'' *Math. Gaz.* **36**, 263-266, 1952.

Freudenthal, H. and van der Waerden, B. L. ``On an Assertion of Euclid.'' *Simon Stevin* **25**, 115-121,
1947.

Gardner, M. *Fractal Music, Hypercards, and More: Mathematical Recreations from Scientific American Magazine.*
New York: W. H. Freeman, pp. 40, 53, and 58-60, 1992.

Pugh, A. *Polyhedra: A Visual Approach.* Berkeley, CA:
University of California Press, pp. 35-36, 1976.

© 1996-9

1999-05-24