Dodecaedru rombohexagonal

Dodecaedru rombohexagonal
(model 3D)
Descriere
Tipparaleloedru
Fețe12 (8 romburi,
      4 hexagoane regulate)
Laturi (muchii)28
Vârfuri18
χ2
Configurația vârfului8 × 4.6.6
8 × 4.4.6
2 × 4.4.4.4
Grup de simetrieD4h, [4,2], (*422), ordinul 16
Grup de rotațieD4, [4,2]+, (422), ordinul 8
Proprietățiconvex
Desfășurată

În geometrie dodecaedrul rombohexagonal[1] sau dodecaedrul alungit,[2] este un dodecaedru convex cu 8 fețe rombice și 4 fețe hexagonale. Hexagoanele pot fi făcute echilaterale, sau regulate, în funcție de forma romburilor. Poate fi văzut ca fiind construit dintr-un dodecaedru rombic, alungit cu o prismă pătrată.

Alături de dodecaedrul rombic, este un poliedru care umple spațiul, unul dintre cele cinci tipuri de paraleloedre identificate de Evgraf Fiodorov și care umplu spațiul față la față prin translații.

Teselări

Acestea sunt legate de fagurele dodecaedric rombic cu alungirea zero. Proiectat normal pe direcția de alungire, fagurele arată ca o pavare pătrată cu romburile proiectate în pătrate.

Variații

Dodecaedrele rombohexagonale pot fi distorsionate în volume cubice, cu fagurele ca o stivă de cuburi deplasate cu o jumătate de latură. De asemenea, pot fi făcute concave deplasând cele 8 colțuri în jos cu aceeași cantitate cu care centrele sunt deplasate în sus.


Poliedru coplanar
Desfășurată
Fagure

Concav
Desfășurată
Fagure

Dodecaedrul rombohexagonal poate fi construit ca o contracție a unui octaedru trunchiat uniform, unde fețele pătrate sunt reduse la laturi, iar fețele hexagonale regulate sunt reduse la fețe rombice cu unghiuri de 60° și 120° (sau perechi de triunghiuri echilaterale). Această construcție alternează pătrate și romburi pe vârfurile cu 4 valențe și are jumătate din simetrie: simetrie D2h, ordinul 8.


Octaedru trunchiat contractat
Desfășurată
Fagure

Note

  1. ^ Williams (1979) p. 169
  2. ^ Coxeter (1973) p. 257

Bibliografie

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