Pentachoric symmetry

Pentachoric symmetry, also known as pennic symmetry and notated as A4, is a 4D spherical Coxeter group. It is the symmetry group of the regular pentachoron.

Convex polytopes with A4 symmetry

 * Pentachoron (regular)
 * Rectified pentachoron (isogonal)/Joined pentachoron (isotopic)
 * Truncated pentachoron (isogonal)/Tetrakis pentachoron (isotopic)
 * Pentapentachoron (isogonal)/Disphenoidal triacontachoron (isotopic)
 * Small rhombated pentachoron (isogonal)/Notched triacontachoron (isotopic)
 * Great rhombated pentachoron (isogonal)/Sphenoidal hexecontachoron (isotopic)
 * Small disprismatopentapentachoron (isogonal)/Triangular-antitegmatic icosachoron (isotopic)
 * Prismatorhombated pentachoron (isogonal)/Rhombipyramidal hexecontachoron (isotopic)
 * Great disprismatopentapentachoron (isogonal)/Tetrahedral hecatonicosachoron (isotopic)