Octàedre truncat

Infotaula de polítopOctàedre truncat
Model 3D
Tipuspolíedre arquimedià, tetradecàedre, políedre uniforme, paral·leloedre i permutàedre Modifica el valor a Wikidata
Forma de les caresquadrat (6)
hexàgon regular (8) Modifica el valor a Wikidata
Símbol de Schläflit{3,4} i tr{3,3} Modifica el valor a Wikidata
Dualcub tetrakis Modifica el valor a Wikidata
Elements
Vèrtexs 24
Arestes 36
Cares 14 Modifica el valor a Wikidata
Més informació
MathWorldTruncatedOctahedron Modifica el valor a Wikidata

En geometria, l'octàedre truncat és un dels tretze políedres arquimedians, s'obté truncant els sis vèrtex de l'octàedre regular.

Té 14 cares, 6 de les quals són quadrades i 8 hexagonals, cada una de les seves 36 arestes separa una cara quadrada d'una hexagonal i a cadascun dels seus 24 vèrtex hi concorren una cara quadrada i dues cares hexagonals.

Àrea i volum

Les fórmules per calcular l'àrea A i el volum V d'un octàedre truncat tal que les seves arestes tenen longitud a són les següents:

Esferes circumscrita, inscrita i tangent a les arestes

Els radis R, r i de les esferes circumscrita, inscrita i tangent a les arestes respectivament són:

On a és la longitud de les arestes.

Dualitat

El políedre dual de l'octàedre truncat és l'hexàedre triakis.

Desenvolupament pla

Desenvolupament pla de l'octàedre truncat


Simetries

El grup de simetria del octàedre truncat té 48 elements; el grup de les simetries que preserven les orientacions és el grup octàedric . Són els mateixos grups de simetria que pel cub i l'octàedre.

Políedres relacionats

La següent successió de políedres il·lustra una transició des del cub a l'octàedre passant per l'octàedre truncat:

Cub
cub
Cub truncat
cub truncat
Cuboctàedre
cuboctàedre
Octàedre truncat
octàedre truncat
Octàedre
octàedre

Vegeu també

Bibliografia

  • H. M. Cundy & A. P. Rollett. I modelli matematici. Milà: Feltrinelli, 1974. 
  • Dedò, Maria. Forme, simmetria e topologia. Bolonya: Decibel & Zanichelli, 1999. ISBN 88-08-09615-7. 

Enllaços externs

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