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Concept
Regular Polytopes
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Summary
Regular Polytopes
are the
Higher-dimensional analogs
of
Regular Polygons
and
Regular Polyhedra
, characterized by their
Symmetrical properties
and
Uniformity in angles
and
Edge lengths
. They exist in any number of dimensions, with the most well-known being the
Platonic Solids
in
Three dimensions
and their generalizations in higher dimensions, such as the hypercube and the simplex.
Concepts
Symmetry
Platonic Solids
Hypercube
Simplex
Dimensionality
Convexity
Euler's Formula
Schläfli Symbol
Coxeter Group
Dual Polytope
Spherical Coxeter Group
Relevant Degrees
Geometry 70%
Algebra 20%
Fundamentals of Mathematics 10%
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