Tesseractic symmetry

Tesseractic symmetry, also known as hexadecachoric symmetry or tessic symmetry and notated as B4 or BC4, is a 4D spherical Coxeter group. It is the symmetry group of the regular tesseract and hexadecachoron.

Subgroups

 * B4+ (maximal)
 * B4/2 (maximal)
 * D4 (maximal)
 * D4+
 * B3×A1 (maximal)
 * (B3×A1)+
 * B3×I
 * B3+×A1
 * B3+×I
 * (B3+×A1)/2
 * (A3+×2×A1)/2
 * (B3×A1)/2
 * A3×A1
 * (A3×A1)+
 * A3×I
 * A3+×2×A1
 * A3+×2×I
 * A3+×A1
 * A3+×I
 * B2≀S2 (maximal)
 * (B2≀S2)+
 * B2×B2
 * (B2×B2)+
 * (B2×B2)/2
 * B2+×B2
 * (B2+×B2)/2
 * B2+≀S2
 * B2+×B2+
 * (B2+×B2+)/2
 * (G2×A1)/2×A1
 * (G2×A1)/2×I
 * (G2+×A1)/2×A1
 * (G2+×A1)/2×I
 * K2×B2
 * (K2×B2)+
 * K2+×B2
 * B2×A1×I
 * B2×I×I
 * (B2×A1)+×A1
 * (B2*A1)+×I
 * K2×B2+
 * K2+×B2+
 * B2+×A1×I
 * B2+×I×I
 * (B2×A1)/2×A1
 * (B2×A1)/2×I
 * (B2+×A1)/2×A1
 * (B2+×A1)/2×I
 * (A2×A1)+×A1
 * (A2×A1)+×I
 * A2×A1×I
 * A2×I×I
 * A2+×A1×I
 * A2+×I×I
 * K2≀S2
 * (K2≀S2)+
 * K2≀S2
 * K4
 * K4+
 * K3×I
 * K3+×A1
 * K3+×I
 * K2+×K2
 * K2+×K2+
 * K2×I×I
 * K2+×A1×I
 * K2+×I×I
 * ±(I×I×I)×I
 * ±(I×I×I×I
 * A1×I×I×I
 * I×I×I×I

Convex polytopes with B4 symmetry

 * Tesseract (regular)/Hexadecachoron (regular)
 * Rectified tesseract (isogonal)/Joined tesseract (isotopic)
 * Rectified hexadecachoron (isogonal)/Joined hexadecachoron (isotopic)
 * Truncated tesseract (isogonal)/Tetrakis hexadecachoron (isotopic)
 * Truncated hexadecachoron (isogonal)/Hexakis tesseract (isotopic)
 * Tesseractihexadecachoron (isogonal)/Disphenoidal enneacontahexachoron (isotopic)
 * Small rhombated tesseract (isogonal)/Notched enneacontahexachoron (isotopic)
 * Small rhombated hexadecachoron (isogonal)/Small notched enneacontahexachoron (isotopic)
 * Great rhombated tesseract (isogonal)/Sphenoidal hecatonenneacontadichoron (isotopic)
 * Great rhombated hexadecachoron (isogonal)/Small sphenoidal hecatonenneacontadichoron (isotopic)
 * Small disprismatotesseractihexadecachoron (isogonal)/Triangular-antitegmatic hexacontatetrachoron (isotopic)
 * Prismatorhombated tesseract (isogonal)/Deltopyramidal hecatonenneacontadichoron (isotopic)
 * Prismatorhombated hexadecachoron (isogonal)/Rhombipyramidal hecatonenneacontadichoron (isotopic)
 * Great disprismatotesseractihexadecachoron (isogonal)/Tetrahedral triacosioctacontatetrachoron (isotopic)