Polyhedron

Pronunciation: /ˌpɒ liˈhi drən/ ?
plural - polyhedra

Polyhedra
Number
of Sides
NameExample
4tetrahedronTetrahedron with four faces that are equilateral triangles.
5pentahedronSquare pyramid with a square base and sloping triangular sides that come to a point on top.
6hexahedronSix sided cube.
7heptahedronA prism with same sized pentagons for top and bottom and straight,rectangular sides.
8octahedronEight congruent triangular faces forming a square at the middle and coming to a point at the ends.
9nonahedronnone
10decahedronTen congruent triangular faces arranged forming a pentagon in the middle and coming to points on the ends.
11undecahedronnone
12dodecahedronA shape with twelve congruent pentagonal faces.
14tetradecahedron
20icosahedronA shape having twenty faces that are congruent equilateral triangles.
24icositetrahedronA shape having twenty-four pentagons as faces.
30triacontahedronA shape with 30 sides. The sides congruent rhomboids.
32icosidodecahedronA shape having 32 sides. Each side is a regular pentagon or an isosceles triangle.
60hexecontahedronA shape having 60 sides that are congruent irregular pentagons.
90enneacontahedronA ninety sided figure with sides that are one of two rhomboids.
Table 1: Polyhedra. Images courtesy Wikipedia Encyclopedia.

A polyhedron is a 3-dimensional shape with sides made of polygons. The simplest polyhedron is the tetrahedron, a four sided figure with each side a triangle. A regular tetrahedron has sides that are equilateral triangles. Polyhedra may be concave or convex. The word polyhedron is from the Greek poly (many) and the Indo-European hedron (seat or face).

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Manipulative 1: Parts of a polyhedron. Created with GeoGebra.

Each polyhedron contains faces, edges, and vertices. A face of a polyhedron is a polygon, a flat, 2-dimensional shape that make up the boundary of the polyhedron. An edge is where 2 faces join. A vertex of a polyhedron is where two or more edges meet.

The Euler-Descarte polyhedron formula relates the number of faces, edges and vertices of convex polyhedra:
V+F-E=2
In the Euler-Descartes formula, V is the number of vertices, F is the number of faces, and E is the number of edges.

Polyhedra are named for the number of sides they possess and, sometimes, the shape of the faces. However, there may be than one shape that qualifies for each name. Click on the image in table 1 to see a larger image. Click on the name in the table to find out more about that class of polyhedra.

More Information

  • Malkevitch, Joseph. Euler's Polyhedral Formula. ams.org. American Mathematical Society. 2010-02-06. http://www.ams.org/featurecolumn/archive/eulers-formula.html.
  • Malkevitch, Joseph. Euler's Polyhedral Formula Part II. ams.org. American Mathematical Society. 2010-02-06. http://www.ams.org/featurecolumn/archive/eulers-formulaII.html.
  • Hart, George W. Virtual Polyhedra. The Encyclopedia of Polyhedra. 2009-03-12. http://www.georgehart.com/virtual-polyhedra/vp.html.

Cite this article as:


Polyhedron. 2009-01-06. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/polyhedron.html.

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Revision History


2009-01-06: Added parts of a polyhedron, and the Euler-Descarte polyhedron formula (McAdams, David.)
2008-09-25: Initial version (McAdams, David.)

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