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Why is $D_5$ a subgroup of the icosahedral group

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#group-theory #finite-groups #symmetry #platonic-solids
1.6k
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What is the result of truncating Platonic solids?

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#geometry #platonic-solids
3.8k
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Five Cubes in Dodecahedron

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#group-theory #polyhedra #platonic-solids
584
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Number of unique cycle paths on an octahedron

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#combinatorics #platonic-solids
110
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Why is a positive angle defect sufficient for the existence of convex regular polytopes?

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#geometry #intuition #polytopes #platonic-solids
124
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Is this solid (gyrate deltoidal icositetrahedron) a fair die?

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#probability #physics #solid-geometry #platonic-solids
299
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Quotient of binary icosahedral group by its center, i.e., $2I/\{\pm 1\}$ is isomorphic to $A_5$

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#abstract-algebra #group-theory #quaternions #platonic-solids #exceptional-isomorphisms
209
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What does "orientation" of a platonic solid really mean?

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#group-theory #geometry #symmetric-groups #symmetry #platonic-solids
262
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What shapes can be made with 144 tetrahedron? Or multiples 288, 432?

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#geometry #solid-geometry #combinatorial-geometry #platonic-solids
315
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Proof of the existance of Platonic Solids other than in Euclids 13 Elements

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#geometry #solid-geometry #platonic-solids
597
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Suggested name for "inflated" tetrahedron

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#geometry #combinatorial-geometry #solid-geometry #simplex #platonic-solids
426
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what abstract regular polyhedra exist?

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#geometry #polyhedra #polytopes #platonic-solids
472
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Determine the length of a side of an octahedron from the volume

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#geometry #platonic-solids
70
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Is there any mathematical formula to find the coordinates of equidistant poins on the surface of a sphere?t

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#group-theory #solid-geometry #platonic-solids
513
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Fitting a dodecahedron inside a cube

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#3d #polyhedra #solid-geometry #platonic-solids

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