Grande cubicubottaedro

Grande cubicubottaedro
TipoPoliedro stellato uniforme
Forma facce8 triangoli
6 quadrati
6 ottagrammi
Nº facce20
Nº spigoli48
Nº vertici24
Caratteristica di Eulero-4
Incidenza dei vertici3.8/3.4.8/3
Notazione di Wythoff3 4 | 4/3
4 3/2 | 4
Diagramma di Coxeter-Dynkin
Gruppo di simmetriaOh, [4,3], *432
DualeGrande icositetraedro esacronico
ProprietàNon convessità
Politopi correlati
Figura al vertice
Poliedro duale

In geometria, il grande cubicubottaedro è un poliedro stellato uniforme avente 20 facce - 8 triangolari, 6 quadrate e 6 forma di ottagramma - 48 spigoli e 24 vertici.[1]

Costruzioni di Wythoff

Utilizzando la costruzione di Wythoff, il grande cubicubottaedro si può ottenere utilizzando tre famiglie di triangoli di Schwarz: 3 4 | 4/3 e 4 3/2 | 4, ottenendo sempre lo stesso risultato.

Coordinate cartesiane

Le coordinate cartesiane per i vertici del grande cubicubottaedro sono date da tutte le permutazioni di:

Poliedri correlati

Il grande cubicubottaedro, spesso indicato con il simbolo U14, ha la stessa disposizione di vertici del cubo troncato, il suo inviluppo convesso; inoltre, esso condivide anche la posizione degli spigoli con il grande rombicubottaedro stellato, avendo in comune con esso la disposizione delle facce triangolari e di 6 facce quadrate, e con il grande rombiesaedro, con cui condivide la disposizione delle facce ottagrammiche.


Cubo troncato

Grande rombicubottaedro stellato

Grande cubicubottaedro

Grande rombiesaedro

Grande icositetraedro esacronico

Grande icositetraedro esacronico
TipoPoliedro stellato
Forma facceAntiparallelogrammi
Nº facce24
Nº spigoli48
Nº vertici20
Caratteristica di Eulero-4
Gruppo di simmetriaOh, [4,3], *432
DualeGrande cubicubottaedro

Il grande icositetraedro esacronico è un poliedro stellato isoedro, nonché il duale del grande cubicubottaedro, avente per facce 24 aquiloni.[2]

Dato un grande cubicubottaedro di spigolo pari a 1, immaginando il grande grande icositetraedro esacronico come composto da 24 facce intersecanti a forma di aquilone, come riportato nella figura sottostante, di cui solo una parte visibile all'esterno del solido, le facce risultanti hanno una coppia di angoli uguali di ampiezza pari a e due angoli di ampiezza e , con il rapporto tra lati lunghi e lati corti pari a .

Note

  1. ^ Roman Maeder, 14: great cubicuboctahedron, su Mathconsult. URL consultato il 24 marzo 2024.
  2. ^ Magnus J. Wenninger, Dual Models, Cambridge University Press, 2004, pp. 58. URL consultato il 20 marzo 2024.

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