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.

Subgroups

 * A4+ (maximal)
 * A3×I (maximal)
 * A3+×I
 * A2×A 1,?sub>×I (maximal)
 * (A2×A1)+×I
 * A2+×A1×I
 * Extended 5-2 step prismatic symmetry (maximal)
 * 5-2 step prismatic symmetry
 * (B2×A1)/2×I
 * (B2+×A1)/2×I
 * A2×I×I
 * A2+×I×I
 * K3×I+
 * K2×I×I
 * K2+×I×I
 * A1×I×I×I
 * I×I×I×I

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)