Grande rombicubottaedro stellato

Grande rombicubottaedro stellato
TipoPoliedro stellato uniforme
Forma facce8 triangoli
6+12 quadrati
Nº facce26
Nº spigoli48
Nº vertici24
Caratteristica di Eulero2
Incidenza dei vertici4.4.4.3/2
Notazione di Wythoff3/2 4 | 2
3 4/3 | 2
Notazione di Schläflirr{4,3/2}
Diagramma di Coxeter-Dynkin
Gruppo di simmetriaOh, [4,3], *432
DualeGrande icositetraedro trapezoidale
ProprietàNon convessità
Politopi correlati
Figura al vertice
Poliedro duale

In geometria, il grande rombicubottaedro stellato è un poliedro stellato uniforme avente 20 facce - 8 triangolari e 18 quadrate - 48 spigoli e 24 vertici.[1]

Costruzioni di Wythoff

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

Coordinate cartesiane

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

Poliedri correlati

Il grande rombicubottaedro stellato, spesso indicato con il simbolo U17, ha la stessa disposizione di vertici del cubo troncato, il suo inviluppo convesso; inoltre, esso condivide anche la posizione degli spigoli con il grande cubicubottaedro, 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 12 facce quadrate.


Cubo troncato

Grande rombicubottaedro stellato

Grande cubicubottaedro

Grande rombiesaedro

Grande icositetraedro trapezoidale

Grande icositetraedro trapezoidale
TipoPoliedro stellato
Forma facceDardi
Nº facce24
Nº spigoli48
Nº vertici26
Caratteristica di Eulero2
Gruppo di simmetriaOh, [4,3], *432
DualeGrande rombicubottaedro stellato

Il grande icositetraedro trapezoidale è un poliedro stellato isoedro, nonché il duale del grande rombicubottaedro stellato, avente per facce 24 dardi, detti anche aquiloni non convessi.[2]

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

Note

  1. ^ Roman Maeder, 17: nonconvex great rhombicuboctahedron, su Mathconsult. URL consultato il 24 marzo 2024.
  2. ^ Magnus J. Wenninger, Dual Models, Cambridge University Press, 2004, pp. 59. URL consultato il 20 marzo 2024.

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