Hexateric symmetry

Hexateric symmetry
Rank	5
Space	Spherical
Order	720
Info
Coxeter diagram
Related polytopes
Omnitruncate	Great cellihexahexateron

Hexateric symmetry, also known as hixic symmetry and notated as A₅, is a 5D spherical Coxeter group. It is the symmetry group of the regular hexateron.

Convex polytopes with A₅ symmetry

• Hexateron (regular)
• Rectified hexateron (isogonal)/Joined hexateron (isotopic)
• Hexahexateron (isogonal)/Triangular-duotegmatic icosateron (isotopic)
• Truncated hexateron (isogonal)/Pentakis hexateron (isotopic)
• Bitruncated hexateron (isogonal)/Triangular-scalenic hexecontateron (isotopic)
• Small rhombated hexateron (isogonal)/Triangular-pyramidal tegmatic hexecontateron (isotopic)
• Small birhombihexahexateron (isogonal)/Disphenoidal tegmatic enneacontateron (isotopic)
• Great rhombated hexateron (isogonal)/Triangular-pyramidal pyramidal hecatonicosateron (isotopic)
• Great birhombihexahexateron (isogonal)/Disphenoidal pyramidal hecatonoctacontateron (isotopic)
• Small prismated hexateron (isogonal)/Antitegmatonotched hexecontateron (isotopic)
• Prismatotruncated hexateron (isogonal)/Notch-pyramidal hecatonoctacontateron (isotopic)
• Prismatorhombated hexateron (isogonal)/Rhombiscalenic hecatonoctacontateron (isotopic)
• Great prismated hexateron (isogonal)/Sphenoidal-pyramidal triacosihexecontateron (isotopic)
• Small cellihexahexateron (isogonal)/Tetrahedral-antitegmatic triacontateron (isotopic)
• Celliprismated hexateron (isogonal)/Triangular-antitegmatic pyramidal hecatonicosateron (isotopic)
• Cellirhombihexahexateron (isogonal)/Anticupolanotched hecatonoctacontateron isotopic)
• Celligreatorhombated hexateron (isogonal)/Deltopyramidal pyramidal triacosihexecontateron (isotopic)
• Celliprismatotruncatohexahexateron (isogonal)/Rhombipyramidal pyramidal triacosihexecontateron (isotopic)
• Great cellihexahexateron (isogonal)/Pentachoric heptacosicositeraon (isotopic)