The #Dodecahedron Links To All Platonic Solids
Published 2023-07-03
• #Dodecahedron
• #Icosahedron
• #Cube
• #Octahedron
• #Tetrahedron
The #Dodecahedron and #Icosahedron are #DualPolyhedra.
The #Cube and #Octahedron are #DualPolyhedra.
(Dual polyhedra are those for which the vertices of one, correlate with the centroids of the facets of the other, and vice-virsa.)
The #Cube contains two #Tetrahedra (any corner vertex, in combination with the 3 farthest vertices from it- excluding the opposite vertex... and then all remaining vertices as a #Tetrahedron pointing in the opposite direction).
The #Dodecahedron, for each pair of opposite vertexes, contains vertices of 2 separate cubes (as shown in the video).
Thus, the #Dodecahedron is related to all 4 of the other #PlatonicSolids:
• It is dual polyhedra with the #Icosahedron.
• It contains #Cubes.
• By containing #Cubes, it contains #Tetrahedra.
• The contained #Cubes are dual polyhedra with #Octahedra.
#Math #Mathmatics
#Nature #NatureIsSpeaking #AreWeListening