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Regular polytope facts for kids

Kids Encyclopedia Facts
POV-Ray-Dodecahedron
A dodecahedron, one of the five Platonic solids

In mathematics, a regular polytope is the generalisation of the regular polygon. Like other polytopes it may have any natural number of dimensions. For example, a two-dimensional regular polytope is a regular polygon, and a three-dimensional regular polytope is a regular polyhedron. Like with the regular polygon, there are certain kinds of symmetries. Regular polytopes have regular facets (faces to speak from the 3D viewpoint), and their vertex figures are regular.

The simplest of the six convex regular 4-polytopes are the pentachoron and tesseract.

Regular simplices

Graphs of the 1-simplex to 4-simplex.
1-simplex t0.svg 2-simplex t0.svg 3-simplex t0.svg 4-simplex t0.svg
Line segment Triangle Tetrahedron Pentachoron
  Regular triangle.svg Tetrahedron.svg Schlegel wireframe 5-cell.png

Images for kids

  • 8-cell-simple

    A 3D projection of a rotating tesseract. This tesseract is initially oriented so that all edges are parallel to one of the four coordinate space axes. The rotation takes place in the xw plane.

  • 24cell section anim

    An animated cut-away cross-section of the 24-cell.

  • Hyperbolic orthogonal dodecahedral honeycomb

    A regular dodecahedral honeycomb, {5,3,4}, of hyperbolic space projected into 3-space.

See also

Kids robot.svg In Spanish: Politopo regular para niños

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Regular polytope Facts for Kids. Kiddle Encyclopedia.