Geometric Nomenclature 102

At the most basic level, the system for naming polyhedra is nearly identical to that for naming polygons. Consequently much of this node is a cut and paste effort from Geometric Nomenclature 101. Never fear, polyhedra are inherently more complex than the humble polygon. Thus, the naming of more obscure polyhedra can be an interesting affair.

The -hedron suffix of polyhedron means "seat", but by considering the less literal translational of "face" we can see why objects of many faces are indeed called polyhedrons.


Basic prefixes

Polyhedral (and polygonal) prefixes are of Greek origin. This explains why the prefix relating to seven is hepta- rather than septa-, as 's' in English corresponds to 'h' in Greek.

Units

1 hena-
2 di-
3 tri-
4 tetra
5 penta-
6 hexa-
7 hepta-
8 octa-
9 ennea-

10 decahedron
11 hendecahedron, undecahedron
12 dodecahedron


Teens

13 trisdecahedron
14 tetradecahedron
15 pentadecahedron
16 hexadecahedron
17 heptadecahedron
18 octadecahedron
19 enneadecahedron


Tens

10 decahedron

20 icosahedron
icosi + unit prefix

30 tricontahedron
triconta + unit prefix

40 tetracontahedron
tetraconta + unit prefix

50 pentacontahedron
pentaconta + unit prefix

60 hexacontahedron
hexaconta + unit prefix

70 heptacontahedron
heptaconta + unit prefix

80 octacontahedron
octaconta + unit prefix

90 enneacontahedron
enneaconta + unit prefix

100 hectohedron
hecta + tens prefix + unit prefix

1000 chiliahedron

10000 myriahedron


Not-so-basic prefixes

Often a polygonal term is placed in front of the polyhedron name to indicate face shape. For example, a pentagonal tetracontahedron is a polyhedron of 40 faces, each with 5 sides. Beyond indicating the number of sides on each face, these face descriptors may refer to the shape of each face. Rhombic polyhedron and trapezoidal polyhedron for instance.

You might also see the term -kis at the end of a (numerical) face descriptor. This indicates that the polyhedron in question has been formed by taking a simpler polyhedron and dividing each face into several isosceles triangles.
For example. an icositetrahedon (24 sides) could be formed by taking a cube and dividing each face into 4 triangles, resulting in a tetrakis cube. In this case, the tetra- is redundant so this shape could just be called a kis cube.

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