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Symmetry Lab4AB · ABC Chemistry

Symmetry Lab › Ih › Dodecahedrane

C₂₀H₂₀ Dodecahedrane

Pentagonal dodecahedron · point group Ih · order 120

Open C₂₀H₂₀ in 3D →

Point group
Ih — The full symmetry of a regular icosahedron or dodecahedron: six C5 axes, ten C3 axes, fifteen C2 axes, a centre of inversion and fifteen mirror planes.
Order
120
Operations
E, 12C₅, 12C₅², 20C₃, 15C₂, i, 12S₁₀, 12S₁₀³, 20S₆, 15σ
Shape
Pentagonal dodecahedron
Atoms
40 (C × 20, H × 20)

Symmetry elements of C₂₀H₂₀

  • C₅ (1) — through the centres of two opposite pentagons; also an S₁₀ axis
  • C₅ (2) — through the centres of two opposite pentagons; also an S₁₀ axis
  • C₅ (3) — through the centres of two opposite pentagons; also an S₁₀ axis
  • C₅ (4) — through the centres of two opposite pentagons; also an S₁₀ axis
  • C₅ (5) — through the centres of two opposite pentagons; also an S₁₀ axis
  • C₅ (6) — through the centres of two opposite pentagons; also an S₁₀ axis
  • C₃ (1) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (2) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (3) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (4) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (5) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (6) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (7) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (8) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (9) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₃ (10) — through the centres of two opposite hexagons / three-fold vertices; also an S₆ axis
  • C₂ (1) — through the midpoints of two opposite edges
  • C₂ (2) — through the midpoints of two opposite edges
  • C₂ (3) — through the midpoints of two opposite edges
  • C₂ (4) — through the midpoints of two opposite edges
  • C₂ (5) — through the midpoints of two opposite edges
  • C₂ (6) — through the midpoints of two opposite edges
  • C₂ (7) — through the midpoints of two opposite edges
  • C₂ (8) — through the midpoints of two opposite edges
  • C₂ (9) — through the midpoints of two opposite edges
  • C₂ (10) — through the midpoints of two opposite edges
  • C₂ (11) — through the midpoints of two opposite edges
  • C₂ (12) — through the midpoints of two opposite edges
  • C₂ (13) — through the midpoints of two opposite edges
  • C₂ (14) — through the midpoints of two opposite edges
  • C₂ (15) — through the midpoints of two opposite edges
  • i — centre of inversion
  • σ (1) — one of the fifteen mirror planes
  • σ (2) — one of the fifteen mirror planes
  • σ (3) — one of the fifteen mirror planes
  • σ (4) — one of the fifteen mirror planes
  • σ (5) — one of the fifteen mirror planes
  • σ (6) — one of the fifteen mirror planes
  • σ (7) — one of the fifteen mirror planes
  • σ (8) — one of the fifteen mirror planes
  • σ (9) — one of the fifteen mirror planes
  • σ (10) — one of the fifteen mirror planes
  • σ (11) — one of the fifteen mirror planes
  • σ (12) — one of the fifteen mirror planes
  • σ (13) — one of the fifteen mirror planes
  • σ (14) — one of the fifteen mirror planes
  • σ (15) — one of the fifteen mirror planes
  • S₁₀ (1) — rotate 36°, then reflect
  • S₁₀ (2) — rotate 36°, then reflect
  • S₁₀ (3) — rotate 36°, then reflect
  • S₁₀ (4) — rotate 36°, then reflect
  • S₁₀ (5) — rotate 36°, then reflect
  • S₁₀ (6) — rotate 36°, then reflect
  • S₆ (1) — rotate 60°, then reflect
  • S₆ (2) — rotate 60°, then reflect
  • S₆ (3) — rotate 60°, then reflect
  • S₆ (4) — rotate 60°, then reflect
  • S₆ (5) — rotate 60°, then reflect
  • S₆ (6) — rotate 60°, then reflect
  • S₆ (7) — rotate 60°, then reflect
  • S₆ (8) — rotate 60°, then reflect
  • S₆ (9) — rotate 60°, then reflect
  • S₆ (10) — rotate 60°, then reflect

Structure

  • C–C 1.54 Å, C–H 1.10 Å
  • Twelve pentagonal faces, all C–C–C 108°
  • One equivalent H on every carbon
Dodecahedrane (C20H20) — Ih symmetry elements
Dodecahedrane: symmetry elements of the Ih point group

Other Ih molecules

[B₁₂H₁₂]²⁻closo-Dodecaborate ionC₆₀Buckminsterfullerene

Open in the 3D lab →  ·  All Ih molecules  ·  All point groups