# BookRiff

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## What are the 7 Platonic solids?

They are the tetrahedron, cube, octahedron, dodecahedron and icosahedron.

• The tetrahedron has 6 faces. Each is an equilateral triangle .
• The cube has 6 faces. Each is a square .
• The octahedron has 8 faces. Each is an equilateral triangle.
• The dodecahedron has 12 faces.
• The icosahedron has 20 faces.

## What is an everyday example of a Platonic solid?

Cube has eight vertices with three square faces meeting. Octahedron has six vertices with four triangular faces meeting. Dodecahedron has 20 vertices with three pentagonal faces meeting. Icosahedron has 12 vertices with five triangular faces meeting.

## What does the dodecahedron represent?

The dodecahedron is said to represent the universe; while the other four Platonic solids represent earth, fire, water and air, the five elements.

## What do you do after dodecahedron?

The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively.

## Who first classified the 5 Platonic solids?

These solids were introduced by Plato in his work Timaeus (ca. 350 BCE), in which all then known forms of matter—earth, air, fire, water, and ether—are described as being composed of five elemental solids: the cube, the octahedron, the tetrahedron, the icosahedron, and the dodecahedron.

## Why are Platonic solids called platonic?

Because of Plato’s systematic development of a theory of the universe based on the five regular polyhedra, they became known as the Platonic solids. These are the only geometric solids whose faces are composed of regular, identical polygons.

## Why does the dodecahedron represent the universe?

The dodecahedron corresponds to the UNIVERSE because the zodiac has 12 signs (the constellations of stars that the sun passes through in the course of one year) corresponding to the 12 faces of the dodecahedron.

## What does the tetrahedron represent?

It is made of four perfect triangles, a shape that symbolizes unity and is regarded as the strongest shape. Its vibration is connected to awakening and manifestation. No matter how a tetrahedron is rotated, there is always one corner that strongly points to the sky.

## ¿Qué son los sólidos platónicos?

Los sólidos platónicos, regulares o perfectos son poliedros convexos tal que todas sus caras son polígonos regulares iguales entre sí, y en que todos los ángulos sólidos son iguales. Reciben este nombre en honor al filósofo griego Platón ( ca. 427 a. C. / 428 a. C. – 347 a. C. ), a quien se atribuye haberlos estudiado en primera instancia.

## ¿Cuáles son los vértices de un sólido platónico?

En todos los vértices de un sólido platónico concurren el mismo número de caras y de aristas. Todas las aristas de un sólido platónico tienen la misma longitud. Todos los ángulos diedros que forman las caras de un sólido platónico entre sí son iguales. Todos sus vértices son convexos a los del icosaedro.

## ¿Qué es una esfera en un sólido platónico?

Como consecuencia geométrica de lo anterior, se pueden trazar en todo sólido platónico tres esferas particulares, todas ellas centradas en el centro de simetría del poliedro: Una esfera inscrita, tangente a todas sus caras en su centro. Una segunda esfera tangente a todas las aristas en su centro.

## ¿Qué es un poliedro platónico?

Proyectando los centros de las aristas de un poliedro platónico sobre su esfera circunscrita desde el centro de simetría del poliedro se obtiene una red esférica regular, compuesta por arcos iguales de círculo máximo, que constituyen polígonos esféricos regulares.