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Sólidos de Catalan

Sólidos de Catalan
Nombre: Triaquistetraedro
Dual:Tetraedro truncado
Cara:Triángulos Isósceles
12 caras
18 aristas
8 vértices
Nombre: Rombododecaedro
Dual:Cuboctaedro
Cara:Rombos
12 caras
24 aristas
14 vértices
Nombre: Triaquisoctaedro
Dual:Cubo truncado
Cara:Triángulos Isósceles
24 caras
36 aristas
14 vértices
Nombre: Tetraquishexaedro
Dual:Octaedro truncado
Cara:Triángulos Isósceles
24 caras
36 aristas
14 vértices
Nombre: Icositetraedro deltoidal
Dual:Rombicuboctaedro
Cara:Deltoides
24 caras
48 aristas
26 vértices
Nombre: Hexaquisoctaedro
Dual:Cuboctaedro truncado
Cara:Triángulos escalenos
48 caras
72 aristas
26 vértices
Nombre: Triacontaedro rómbico
Dual:Icosidodecaedro
Cara:Rombos
30 caras
60 aristas
32 vértices
Nombre: Triaquisicosaedro
Dual:Dodecaedro truncado
Cara:Triángulos Isósceles
60 caras
90 aristas
32 vértices
Nombre: Pentaquisdodecaedro
Dual:Icosaedro truncado
Cara:Triángulos isósceles
60 caras
90 aristas
32 vértices
Nombre: Hexecontaedro deltoidal
Dual:Rombicosidodecaedro
Cara:Deltoides
60 caras
120 aristas
62 vértices
Nombre: Hexaquisicosaedro
Dual:Icosidodecaedro truncado
Cara:Triángulos Escalenos
120 caras
180 aristas
62 vértices
Nombre: Icositetraedro pentagonal
Dual:Cubo romo
Cara:Pentágonos Irregulares
24 caras
60 aristas
38 vértices
Nombre: Hexecontaedro pentagonal
Dual:Icosidodecaedro romo
Cara:Pentágonos irregulares
60 caras
150 aristas
92 vértices

Los sólidos de Catalan son una familia de poliedros que se generan con el poliedro dual de los sólidos de Arquímedes; fueron nombrados así por el matemático belga Eugène Charles Catalan.

Todos son poliedros convexos de caras uniformes aunque no de vértices uniformes; esto ocurre ya que los sólidos de Arquímedes que los generan son de vértices uniformes y no de caras uniformes. Las caras que forman un sólido de Catalan no son polígonos regulares, pero sus ángulos diédricos son iguales en todo el poliedro. Además dos de ellos son poliedros de aristas uniformes: el rombododecaedro y el triacontaedro rómbico, y dos de ellos tienen figura isomórfica: el icositetraedro pentagonal y el hexecontaedro pentagonal.

Los sólidos de Catalan son trece (13) en total, así como los sólidos de Arquímedes:

  1. Triaquistetraedro o tetraedro triakis.
  2. Rombododecaedro o dodecaedro rómbico.
  3. Triaquisoctaedro u octaedro triakis.
  4. Tetraquishexaedro o hexaedro tetrakis.
  5. Icositetraedro deltoidal.
  6. Hexaquisoctaedro, disdiaquisdodecaedro, octaedro hexakis o dodecaedro disdiakis.
  7. Triacontaedro rómbico.
  8. Triaquisicosaedro o icosaedro triakis.
  9. Pentaquisdodecaedro o dodecaedro pentakis.
  10. Hexecontaedro deltoidal.
  11. Hexaquisicosaedro, disdiaquistriacontaedro, icosaedro hexakis o triacontaedro disdiakis.
  12. Icositetraedro pentagonal.
  13. Hexecontaedro pentagonal.

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