SUBGROUP VISUALIZER
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O(3)
|
Axis-Angle Ball Model
|
Orbifold Notation
Point Group
332 — chiral tetrahedral
*332 — full tetrahedral
3*2 — pyritohedral
432 — chiral octahedral
*432 — full octahedral
532 — chiral icosahedral
*532 — full icosahedral
22 — 2-fold rotation
33 — 3-fold rotation
44 — 4-fold rotation
66 — 6-fold rotation
*22 — with vertical mirrors
*44 — with vertical mirrors
222 — three 2-folds
224 — 4-fold + two 2-folds
226 — 6-fold + two 2-folds
*222 — with mirrors
*224 — with mirrors
× — inversion (Cᵢ)
2× — S₄ rotoreflection
3× — S₆ (C₃ᵢ)
Rotation Angle
α
= Distance From Origin
0
π/2
π
Element Count
det +1
0
det −1
0
|G|
0
ORBIFOLD KEY:
n
= n-fold cone (rotation axis) ·
*
= mirror boundary ·
×
= cross-cap (roto-reflection) ·
Points at α = π are glued antipodally
LEFT BALL: PROPER ROTATIONS (det +1)
RIGHT BALL: IMPROPER ROTATIONS (det −1)