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Polyhedron

Explore Polyhedron on MathWorld


A polyhedron is a three-dimensional solid that consists of a collection of polygons, joined at their edges.

Polyhedron is a high school-level concept that would be first encountered in a geometry course covering solid geometry.

Examples

Cube: The cube is the Platonic solid comprised of six equal square faces that meet each other at right angles, eight vertices, and twelve edges.
Dodecahedron: (1) A general dodecahedron is any polyhedron having 12 faces. (2) The regular dodecahedron is the Platonic solid comprised of 12 pentagonal faces, 20 vertices, and 30 edges.
Icosahedron: (1) A general icosahedron is any polyhedron having 20 faces. (2) The regular icosahedron is the Platonic solid comprised of 20 equilateral triangles, 12 vertices, and 30 edges.
Octahedron: (1) A general octahedron is any polyhedron having eight faces. (2) The regular octahedron is the Platonic solid comprised of eight equilateral triangular faces, eight edges, and six vertices.
Platonic Solid: The Platonic solids are the five convex solids composed of identical regular polygons.
Pyramid: A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces' triangles meeting at a common polygon vertex (known as the "apex").
Tetrahedron: (1) A general tetrahedron is any polyhedron having four faces. (2) The regular tetrahedron is the Platonic solid comprised of four equilateral triangles, four vertices, and six edges.

Classroom Articles on Solid Geometry

  • Cone
  • Solid Geometry
  • Convex Hull
  • Sphere
  • Cross Section
  • Surface
  • Cylinder
  • Surface Area
  • Prism
  • Volume

  • Classroom Articles on Geometry (Up to High School Level)

  • Acute Angle
  • Linear Function
  • Altitude
  • Midpoint
  • Angle
  • Nonagon
  • Area
  • Obtuse Angle
  • Circle
  • Octagon
  • Circumference
  • Parallel
  • Collinear
  • Parallelogram
  • Complementary Angles
  • Pentagon
  • Congruent
  • Perimeter
  • Decagon
  • Perpendicular
  • Diameter
  • Pi
  • Dodecagon
  • Plane Geometry
  • Equilateral Triangle
  • Point
  • Geometric Construction
  • Polygon
  • Geometry
  • Polytope
  • Golden Ratio
  • Quadrilateral
  • Golden Rectangle
  • Radius
  • Hendecagon
  • Rectangle
  • Heptagon
  • Regular Polygon
  • Hexagon
  • Right Triangle
  • High-Dimensional Solid
  • Similar
  • Hypercube
  • Square
  • Hyperplane
  • Supplementary Angles
  • Hypersphere
  • Trapezoid
  • Hypotenuse
  • Triangle
  • Isosceles Triangle
  • Triangle Inequality