The only irreducible spherical simplexes generated by reflection are (), (), (), (, , , , , , and . The only irreducible Euclidean simplexes generated by reflection are , (), (), (), (), , , , , and .
Spherical Simplex
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Cite this as:
Weisstein, Eric W. "Spherical Simplex." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SphericalSimplex.html