Chiral tetrahedral symmetry

Chiral tetrahedral symmetry
Rank	3
Space	Spherical
Order	12
Elements
Axes	3 × A1×A1×A1+, 4 × A2+×I

Chiral tetrahedral symmetry, also known as kitettic symmetry and notated A₃+ is a 3D spherical symmetry group. It is the symmetry group of the tetrahedron with all the reflections removed.

Subgroups

• Chiral triangular pyramidal symmetry (maximal)
• Chiral digonal prismatic symmetry (maximal)
• Chiral digonal pyramidal symmetry
• Identity symmetry

Convex polytopes with A₃+ symmetry

• Tetrahedron (regular)
• Tetratetrahedron (isogonal)/Triangular antitegum (isotopic)
• Truncated tetrahedron (isogonal)/Triakis tetrahedron (isotopic)
• Rhombitetratetrahedron (isogonal)/Deltoidal dodecahedron (isotopic)
• Snub tetrahedron (isogonal)/Tetartoid (isotopic)