The most complicated Platonic solid
is the icosahedron (the shape of 20-sided dice).
Interestingly, either the shape of the face is a triangle, which has three sides (tetrahedron, octahedron, icosahedron) or three faces come together at the vertices (tetrahedron, cube, dodecahedron) or both (tetrahedron) to form the Platonic solid
(see Figure 3B for example of the cube).
An Archimedean solid can be derived from a Platonic solid
by simultaneous truncation of all the vertices of the Platonic solid
But because the faces of the cube can be easily subdivided into square quadtrees, it was chosen as the base platonic solid
by Alborzi and Samet (2000).
Just why dimension four has an extra platonic solid
is a puzzle to mathematicians.
LOS ANGELES, July 16, 2015 /PRNewswire/ -- The Astar Collection contains pillows, a bench, stool and barstool each with a different quilted fractal design based on one of the five platonic solids
A few among them have been mathematicians who have obsessed about Platonic solids
, a class of geometric forms that are highly regular and are commonly found in nature.
Working with consulting curator Srdjan Jovanovic Weiss, the ninety-year-old architect has designed inhabitable sculptures for the exhibition that build on her long-standing interest in Platonic solids
I am going to risk pushing this analogy to an extreme and say that it was as if Wedel conceptually played around with philosophical thinking of the ancient Greeks and made clay versions of the forms of the Platonic solids
that they believed to be the elemental shapes that comprised the stuff of the world (especially those highly complex shapes like multi-faceted dodecahedrons and icosahedrons) that he then threw together willy-nilly to create the ceramic objects that become his gems.
After reviewing the classical treatments of Golden Mean, Fibonacci numbers, and Platonic solids
, he covers the mathematics of harmony and its application in computer science.
One can devise another application: assign different letters to the links on the Platonic solids
, such that each node has a word consisting of the letters of its incoming links.
A Geometric Analysis of the Platonic Solids
and Other Semi-Regular Polyhedra