page_title: Point groups in four dimensions
section_title: Chiral subgroups
hierarchical_section_title: Point groups in four dimensions / Notation for groups / Chiral subgroups
caption_attribution_description: English: Stereographic projection of the 600-cell, a 4-dimensional polytope. Vertices and edges are shown; faces are not. author: Fritz Obermeyer Cell-Centere stereographic projection. The 720 edges of the 600-cell can be seen here as 72 circles, each divided into 10 arc-edges at the intersections. Each vertex has 6 circles intersecting. url: http://www.math.cmu.edu/~fho/jenn/polytopes/600-cell.png
context_page_description: In geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere.
context_section_description: Direct subgroups of the reflective 4-dimensional point groups are:
caption: The 600-cell edges projected onto a 3-sphere represent 72 great circles of H4 symmetry. Six circles meet at each vertex. Each circle represent axes of 5-fold symmetry.
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