Grande rombiesaedro

Grande rombiesaedro
TipoPoliedro stellato uniforme
Forma facce12 quadrati
6 ottagrammi
Nº facce18
Nº spigoli48
Nº vertici24
Caratteristica di Eulero-6
Incidenza dei vertici4.8/3.4/3.8/5
Notazione di Wythoff2 4/3 (3/2 4/2) |
Diagramma di Coxeter-Dynkin
Gruppo di simmetriaOh, [4,3], *432
DualeGrande rombiesacrono
ProprietàNon convessità
Politopi correlati
Figura al vertice
Poliedro duale

In geometria, il grande rombiesaedro è un poliedro stellato uniforme avente 18 facce - 12 quadrate e 6 forma di ottagramma - 48 spigoli e 24 vertici.[1]

Costruzioni di Wythoff

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

Coordinate cartesiane

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

Poliedri correlati

Il grande rombiesaedro, spesso indicato con il simbolo U21, 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 12 facce quadrate, e con il grande cubicubottaedro, con cui condivide la disposizione delle facce ottagrammiche.


Cubo troncato

Grande rombicubottaedro stellato

Grande cubicubottaedro

Grande rombiesaedro

Grande rombiesacrono

Grande rombiesacrono
TipoPoliedro stellato
Forma facceAntiparallelogrammi
Nº facce24
Nº spigoli48
Nº vertici18
Caratteristica di Eulero-6
Gruppo di simmetriaOh, [4,3], *432
DualeGrande rombiesaedro

Il grande rombiesacrono è un poliedro stellato isoedro, nonché il duale del grande rombiesaedro, avente per facce 24 antiparallelogrammi.[2]

Dato un grande rombiesaedro di spigolo pari a 1, immaginando il grande rombiesacrono come composto da 24 facce intersecanti a forma di antiparallelogramma, come riportato nella figura sottostante, di cui solo una parte visibile all'esterno del solido, le facce risultanti hanno due coppie di angoli uguali di ampiezza pari a e , con il rapporto tra lati lunghi e lati corti pari a e le due diagonali che si incontrano con un angolo di .

Note

  1. ^ Roman Maeder, 21: great rhombihexahedron, su Mathconsult. URL consultato il 24 marzo 2024.
  2. ^ Magnus J. Wenninger, Dual Models, Cambridge University Press, 2004, pp. 60. URL consultato il 20 marzo 2024.

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