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Platonic Solid

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The Platonic solids are the five convex solids composed of identical regular polygons.

Platonic solid 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.
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.

Prerequisites

Regular Polygon: A regular polygon is a polygon in which the sides are all the same length and the angles all have the same measure.

Classroom Articles on Solid Geometry

  • Cone
  • Pyramid
  • Convex Hull
  • Solid Geometry
  • Cross Section
  • Sphere
  • Cylinder
  • Surface
  • Polyhedron
  • 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
  • Right Triangle
  • Hexagon
  • Similar
  • High-Dimensional Solid
  • Square
  • Hypercube
  • Supplementary Angles
  • Hyperplane
  • Trapezoid
  • Hypersphere
  • Triangle
  • Hypotenuse
  • Triangle Inequality
  • Isosceles Triangle