Mensaje de error

  • Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of /homepages/3/d408889334/htdocs/sg/includes/file.phar.inc).
  • Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of /homepages/3/d408889334/htdocs/sg/includes/file.phar.inc).
  • Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of /homepages/3/d408889334/htdocs/sg/includes/file.phar.inc).
  • Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of /homepages/3/d408889334/htdocs/sg/includes/file.phar.inc).
  • Deprecated function: session_set_save_handler(): Providing individual callbacks instead of an object implementing SessionHandlerInterface is deprecated in drupal_session_initialize() (line 242 of /homepages/3/d408889334/htdocs/sg/includes/session.inc).
  • Deprecated function: SelectQueryInterface::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: SelectQueryInterface::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: SelectQueryExtender::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: SelectQueryExtender::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: SelectQuery::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: DrupalEntityControllerInterface::resetCache(): Implicitly marking parameter $ids as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: DrupalDefaultEntityController::resetCache(): Implicitly marking parameter $ids as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 3542 of /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: menu_tree_prune_tree(): Implicitly marking parameter $parent_item as nullable is deprecated, the explicit nullable type must be used instead en include_once() (línea 1439 de /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: DrupalDefaultMetaTag::__construct(): Implicitly marking parameter $data as nullable is deprecated, the explicit nullable type must be used instead en include_once() (línea 3542 de /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).
  • Deprecated function: DrupalListMetaTag::__construct(): Implicitly marking parameter $data as nullable is deprecated, the explicit nullable type must be used instead en include_once() (línea 3542 de /homepages/3/d408889334/htdocs/sg/includes/bootstrap.inc).

Sólidos Platónicos

Existen sólo cinco poliedros que se puedan construir usando un polígono regular como cara y con el mismo número de caras en cada vértice. Los cinco Sólidos Platónicos son el tetraedro, cubo, octaedro, icosaedro y dodecaedro (Figura 1).

 

TETRAEDRO CUBO OCTAEDRO ICOSAEDRO DODECAEDRO
Figura 1: Los Sólidos Platónicos. Hacer Click para ver un Modelo 3D que se puede ampliar y rotar.

 

La siguiente tabla describe las propiedades principales de los Sólidos Platónicos. El Dual de un sólido es el poliedro que se obtiene al unir los centros de las caras adyacentes; así pues, el dual tiene el número de vértices y aristas intercambiados. El Coeficiente constructivo tridimensional da una idea de la complejidad de un sólido.

 

SOLIDO PLATONICO IMAGEN NUMERO DE CARAS CARAS POR VERTICE VERTICES ARISTAS COEFICIENTE CONSTRUCTIVO TRIDIMENSIONAL SOLIDO DUAL IMAGEN

tetraedro

 4 3 4 6 1 tetraedro
cubo 6 3 8 12 2 octaedro
octaedro 8 4 6 12 2 cubo
icosaedro 20 5 12 30 5 dodecaedro
dodecaedro 12 3 20 30 5 icosaedro
Tabla 1: Propiedades principales de los Sólidos Platónicos