page_title: Final stellation of the icosahedron
section_title: Interpretations
hierarchical_section_title: Final stellation of the icosahedron / Interpretations
caption_attribution_description: English: Diagram for The fifty nine icosahedra
context_page_description: In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram. That is, every three intersecting face planes of the icosahedral core intersect either on a vertex of this polyhedron, or inside of it.
  This polyhedron is the seventeenth stellation of the icosahedron, and given as Wenninger model index 42.
  As a geometrical figure, it has two interpretations, described below:
  As an irregular star polyhedron with 20 identical self-intersecting enneagrammic faces, 90 edges, 60 vertices.
  As a simple polyhedron with 180 triangular faces, 270 edges, and 92 vertices. This interpretation is useful for polyhedron model building.
  Johannes Kepler researched stellations that create regular star polyhedra in 1619, but the complete icosahedron, with irregular faces, was first studied in 1900 by Max Brückner.
caption: Stellation diagram of the icosahedron with numbered cells. The complete icosahedron is formed from all the cells in the stellation, but only the outermost regions, labelled "13" in the diagram, are visible.
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