Tesseractic symmetry
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| Tesseractic symmetry | |
|---|---|
| Rank | 4 |
| Space | Spherical |
| Order | 384 |
| Info | |
| Coxeter diagram |    |
| Related polytopes | |
| Omnitruncate | Great disprismatotesseractihexadecachoron |
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[edit | edit source]
- 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[edit | edit source]
- 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)