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Most polyhedra are unbelievably complicated, because there are infinitely many large numbers but only finitely many small numbers. So the polyhedra with gazillions of faces far outnumber the polyhedra with, say, 20 faces. For example, the Great Prismosaurus section displayed at the beginning of my four-dimensional uniform polytopes website has only about 700 faces, but each face is diced up by the other faces into innumerable external facelets, making it so complicated that a physical model probably could not be built with existing technology. Fortunately, many interesting polyhedra have a manageable number of faces and can be modeled successfully in paper.

What makes a polyhedron interesting?

The most famous constraints on a polyhedron are that all its faces be congruent regular polygons and that the same arrangement of faces exist around each vertex. Of all the uncountably infinite possible polyhedra, only nine different kinds satisfy these conditions: the

If we relax the constraint on the regular polyhedra to have all the faces necessarily be congruent, but retain the constraints to have the faces be regular polygons and to have the same arrangement of faces at each vertex, the resulting polyhedra are known as

Greek Numerical Prefixes | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

UNITS | TEENS | TWENTIES | THIRTIES-PLUS | HUNDREDS | THOUSANDS | ||||||

10 | deca- | 20 | icosa- | 30 | triaconta- | 100 | hecaton- | 1000 | chilia- | ||

1 | mono- | 11 | hendeca- | 21 | icosimono- | 31 | triacontamono- | 200 | diacosi- | 2000 | dischilia- |

2 | di- | 12 | dodeca- | 22 | icosidi- | 32 | triacontadi- | 300 | triacosi- | 3000 | trischilia- |

3 | tri- | 13 | trideca- | 23 | icositri- | 33 | triacontatri- | 400 | tetracosi- | 4000 | tetrakischilia- |

4 | tetra- | 14 | tetradeca- | 24 | icositetra- | 40 | tetraconta- | 500 | pentacosi- | 5000 | pentakischilia- |

5 | penta- | 15 | pentadeca- | 25 | icosipenta- | 50 | penteconta- | 600 | hexacosi- | 6000 | hexakischilia- |

6 | hexa- | 16 | hexadeca- | 26 | icosihexa- | 60 | hexeconta- | 700 | heptacosi- | 7000 | heptakischilia- |

7 | hepta- | 17 | heptadeca- | 27 | icosihepta- | 70 | hebdomeconta- | 800 | octacosi- | 8000 | octakischilia- |

8 | octa- | 18 | octadeca- | 28 | icosiocta- | 80 | ogdoeconta- | 900 | enacosi- | 9000 | enakischilia- |

9 | ennea- | 19 | enneadeca- | 29 | icosiennea- | 90 | eneneconta- | 10000 | myria- |

Other variations are possible, but these follow a fairly regular pattern and are compatible with names in common use for polygons and polyhedra.

Link to these pages to view this website fully and to see more photographs of polyhedron models:

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