Grande icosidodecaedro camuso

Grande icosidodecaedro camuso
TipoPoliedro stellato uniforme
Forma facce20+60 triangoli
12 pentagrammi
Nº facce92
Nº spigoli150
Nº vertici60
Caratteristica di Eulero2
Incidenza dei vertici34.5/2
Notazione di Wythoff| 2 5/2 3
Diagramma di Coxeter-Dynkin
Gruppo di simmetriaI, [5,3]+, 532
DualeGrande esacontaedro pentagonale
ProprietàNon convessità
Politopi correlati
Figura al vertice
Poliedro duale

In geometria, il grande icosidodecaedro camuso è un poliedro stellato uniforme avente 92 facce - 80 triangolari e 12 a forma di pentagramma - 150 spigoli e 60 vertici.[1]

Coordinate cartesiane

Le coordinate cartesiane per i vertici del grande icosidodecaedro camuso, spesso indicato con il simbolo U57 e il cui inviluppo convesso è un dodecaedro camuso non uniforme, sono date da tutte le permutazioni pari di:

con un numero pari di segni più, dove è la sezione aurea, è la soluzione negativa dell'equazione e

Poliedri correlati

Dato un grande icosidodecaedro camuso di spigolo pari a 1, il suo circumraggio è pari a dove è la seconda più grande radice reale dell'equazione

Le quattro radici positive dell'equazione in , sono, in ordine, i circumraggi del grande icosidodecaedro retrocamuso (U74), del grande icosidodecaedro camuso (U57), del grande icosidodecaedro camuso invertito (U69) e del dodecaedro camuso (U29).

Grande esacontaedro pentagonale

Grande esacontaedro pentagonale
TipoPoliedro stellato
Forma faccePentagoni irregolari
Nº facce60
Nº spigoli150
Nº vertici92
Caratteristica di Eulero2
Gruppo di simmetriaI, [5,3]+, 532
DualeGrande icosidodecaedro camuso

Il grande esacontaedro pentagonale è un poliedro stellato isoedro, nonché il duale del grande icosidodecaedro camuso, avente per facce 60 pentagoni irregolari.[2]

Dato un grande icosidodecaedro camuso di spigolo pari a 1, immaginando il grande esacontaedro pentagonale come composto da 60 facce intersecanti a forma di pentagono irregolare, come riportato nella figura sottostante, di cui solo una parte visibile all'esterno del solido, e considerando la già citata sezione aurea e il numero - radice negativa del polinomio , ogni faccia risulta avere quattro angoli uguali di ampiezza pari a e uno angolo di ampiezza pari a - con tre lati lunghi e due corti le cui lunghezze stanno in un rapporto pari a

Note

  1. ^ Roman Maeder, 57: great snub icosidodecahedron, su Mathconsult. URL consultato il 24 marzo 2024.
  2. ^ Magnus J. Wenninger, Dual Models, Cambridge University Press, 2004, pp. 123. URL consultato il 20 marzo 2024.

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