Ortobicupolă triunghiulară alungită

Ortobicupolă triunghiulară alungită
(model 3D)
Descriere
Tippoliedru Johnson
J34 – J35 – J36
Fețe20 (8 triunghiuri echilaterale,
      12 pătrate)[1]
Laturi (muchii)36[1]
Vârfuri18[1]
χ2
Configurația vârfului6 (3.4.3.4); 12 (3.43)
Grup de simetrieD3h, [3,2], (*223), ordin 12
Arie≈ 15,464 a2   (a = latura)
Volum  ≈ 4,955 a3   (a = latura)
Poliedru dual–
Proprietățiconvexă
Desfășurată

În geometrie ortobicupola triunghiulară alungită sau prisma triunghiulară cantelată este un poliedru convex construit prin alungirea unei ortobicupole triunghiulare (J27) prin inserarea unei prisme hexagonale între cele două jumătăți. Este poliedrul Johnson J35.[1][2] Având 20 de fețe, este un tip de icosaedru. Deoarece această denumire se referă de obicei la icosaedrul regulat, rareori este folosită fără precizări suplimentare.

Poliedrul rezultat este oarecum similar cu rombicuboctaedrul (unul dintre poliedrele arhimedice), cu diferența că are simetrie de rotație cu trei poziții în jurul axei sale în loc de simetrie cu patru poziții.

Mărimi asociate

Următoarele formule pentru arie, A și volum, V sunt stabilite pentru lungimea laturilor tuturor poligoanelor (care sunt regulate) a:[1]

Poliedre și faguri înrudiți

Ortobicupola triunghiulară alungită formează faguri cu tetraedre și piramide pătrate.[3]

Note

  1. ^ a b c d e en Stephen Wolfram, "Elongated triangular orthobicupola" from Wolfram Alpha. Retrieved December 11, 2022.
  2. ^ en Johnson, Norman W. (), „Convex polyhedra with regular faces”, Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603 
  3. ^ en „J35 honeycomb”. 

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