![Space–time lift diagram for g130 and polar space group No. 101 P4_2cm; exact clock phases form stacked sheets in vertical time through one clock period. Activate the interactive viewer to examine [Me4N][Cu2(NCS)3].](output/space-groups/g130.webp?v=stacked-clock-period)
Diagram key
Crystallographic generator symbols: visual index
Projected along the clock axis, these are the actual symbols used on the static 2D diagrams. Open arrows mark primitive translations in the picture; the crystallographic filled core shows the 2-, 3-, 4-, or 6-fold spatial order. For a forward skip τ, the screw subscript is m ≡ nτ (mod n) for a positive 1/n-turn and m ≡ −nτ (mod n) for the opposite turn, with 0 ≤ m < n. Screw tails prolong the polygon edges, as in the Tables; a mirrored pinwheel records the opposite spatial turn sense, not backward time.
Translations in the projection plane
- Primitive translationOpen arrow; its direction is the named in-plane translation X, Y, or α.
Rotation and screw axes (along the clock axis)
- 2-fold rotation axisFilled lens; half-turn with no clock-axis rise.
- 21 screw axisTwo-arm lens; half-turn with a +1/2-period rise.
- 3-fold rotation axisFilled triangle; one-third turn with no clock-axis rise.
- 31 screw axisThree-stroke triangle; positive one-third turn with a +1/3-period rise.
- 32 screw axisOpposite three-stroke triangle; positive one-third turn with a +2/3-period rise.
- 4-fold rotation axisFilled diamond; quarter-turn with no clock-axis rise.
- 41 screw axisFour-arm diamond; positive quarter-turn with a +1/4-period rise.
- 42 screw axisTwo-arm diamond; quarter-turn with a +1/2-period rise.
- 43 screw axisOpposite four-arm diamond; positive quarter-turn with a +3/4-period rise.
- 6-fold rotation axisFilled hexagon; one-sixth turn with no clock-axis rise.
- 61 screw axisSix-arm hexagon; positive one-sixth turn with a +1/6-period rise.
- 62 screw axisThree-arm hexagon; positive one-sixth turn with a +1/3-period rise.
- 63 screw axisTwo-arm hexagon; one-sixth turn with a +1/2-period rise.
- 64 screw axisOpposite three-arm hexagon; positive one-sixth turn with a +2/3-period rise.
- 65 screw axisOpposite six-arm hexagon; positive one-sixth turn with a +5/6-period rise.
Mirror and glide planes (seen edge-on)
- Mirror plane (m)Solid line; reflection with no glide component.
- In-plane axial glideDashed line with a half arrow; reflection plus a half-cell step, the arrow giving the direction of that step.
- Clock-axis glide (c)Dotted line; reflection plus a half-period step perpendicular to the picture.
- Diagonal n-glideDash–dot line; half-steps in the picture and along the clock axis.
- Quarter-diagonal d-glideArrowed dash–dot line; arrows select the sign of the quarter-period component.
The burgundy α, β, γ, … or P, Q, … beside a diagram symbol identifies its Generator row. The Color and Time columns state the same forward clock action directly.
Notation: International Tables for Crystallography projection symbols · UCL P 3 1 c example.