Triangular tiling - Revision history

Muzik: /* Kinetic */

2026-07-20T15:32:52Z

Kinetic

← Older revision		Revision as of 15:32, 20 July 2026
Line 203:		Line 203:
	\| Pattern has C2_4 symmetry<br>Appears flipped across both a diagonal and orthogonal line during (period/2)<br>Lines intersect at the center of an edge		\| Pattern has C2_4 symmetry<br>Appears flipped across both a diagonal and orthogonal line during (period/2)<br>Lines intersect at the center of an edge
	\| 1 diagonal<br>p/2		\| 1 diagonal<br>p/2
	\|-
	~~! C3_1~~
	~~! C6~~
	~~\| 2~~
	~~\| Pattern has C3_1 symmetry<br>Appears rotated 60 degrees during (period/2)<br>Rotation is centered on a vertex~~
	~~\| none~~
	\|-		\|-
	! C3_1		! C3_1
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	\| Pattern has C3_1 symmetry<br>Appears flipped across one of three diagonal lines during (period/2)<br>Lines intersect at a vertex		\| Pattern has C3_1 symmetry<br>Appears flipped across one of three diagonal lines during (period/2)<br>Lines intersect at a vertex
	\| 3 diagonals<br>p/2		\| 3 diagonals<br>p/2
			\|-
			! C3_1
			! C6
			\| 2
			\| Pattern has C3_1 symmetry<br>Appears rotated 60 degrees during (period/2)<br>Rotation is centered on a vertex
			\| none
	\|-		\|-
	! C3_3		! C3_3

Gzaytman at 02:58, 4 July 2026

2026-07-04T02:58:15Z

← Older revision		Revision as of 02:58, 4 July 2026
Line 333:		Line 333:
	}}		}}

	[[Category:Euclidean tilings]] [[Category:Triangular rules]]		[[Category:Euclidean tilings]] [[Category:Triangular rules\| ]]

Neocaridina at 10:52, 12 February 2026

2026-02-12T10:52:08Z

← Older revision		Revision as of 10:52, 12 February 2026
Line 333:		Line 333:
	}}		}}

	[[Category:Euclidean tilings]]		[[Category:Euclidean tilings]] [[Category:Triangular rules]]

Muzik: /* Bounded grids */

2025-10-13T10:23:05Z

Bounded grids

← Older revision		Revision as of 10:23, 13 October 2025
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	A regular hexagon composed of smaller triangles can tile the grid purely through translation, permitting toroidal bounded grids at the very least.		A regular hexagon composed of smaller triangles can tile the grid purely through translation, permitting toroidal bounded grids at the very least.

	As all known programs only use ~~square~~ bounded grids so far, the characteristics remain unknown.		As all known programs only use rectangular bounded grids so far, the characteristics remain unknown.

	=== Coordinates, displacement notation and static and kinetic symmetries ===		=== Coordinates, displacement notation and static and kinetic symmetries ===

Gzaytman: /* Kinetic */

2025-10-13T06:22:12Z

Kinetic

← Older revision		Revision as of 06:22, 13 October 2025
Line 166:		Line 166:
	\| 2		\| 2
	\| Pattern has D2_xo symmetry<br>Appears flipped across a diagonal line during (period/2)<br>Lines intersect at a vertex		\| Pattern has D2_xo symmetry<br>Appears flipped across a diagonal line during (period/2)<br>Lines intersect at a vertex
	\|		\| 1 diagonal<br>p/2
	\|-		\|-
	! D2_xo		! D2_xo
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	\| 2		\| 2
	\| Pattern has D2_xo symmetry<br>Appears flipped across a diagonal line during (period/2)<br>Lines intersect at the center of an edge		\| Pattern has D2_xo symmetry<br>Appears flipped across a diagonal line during (period/2)<br>Lines intersect at the center of an edge
	\|		\| 1 diagonal<br>p/2
	\|-		\|-
	! D2_x		! D2_x
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	\| 2		\| 2
	\| Pattern has D2_x symmetry<br>Appears flipped across an orthogonal line during (period/2)<br>Lines intersect at a vertex		\| Pattern has D2_x symmetry<br>Appears flipped across an orthogonal line during (period/2)<br>Lines intersect at a vertex
	\|		\| none
	\|-		\|-
	! D2_x		! D2_x
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	\| 2		\| 2
	\| Pattern has C2_1 symmetry<br>Appears flipped across both a diagonal and orthogonal line during (period/2)<br>Lines intersect at a vertex		\| Pattern has C2_1 symmetry<br>Appears flipped across both a diagonal and orthogonal line during (period/2)<br>Lines intersect at a vertex
	\|		\| 1 diagonal<br>p/2
	\|-		\|-
	! C2_1		! C2_1
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	\| 2		\| 2
	\| Pattern has C2_4 symmetry<br>Appears flipped across both a diagonal and orthogonal line during (period/2)<br>Lines intersect at the center of an edge		\| Pattern has C2_4 symmetry<br>Appears flipped across both a diagonal and orthogonal line during (period/2)<br>Lines intersect at the center of an edge
	\|		\| 1 diagonal<br>p/2
	\|-		\|-
	! C3_1		! C3_1
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	\| 2		\| 2
	\| Pattern has C3_1 symmetry<br>Appears flipped across one of three diagonal lines during (period/2)<br>Lines intersect at a vertex		\| Pattern has C3_1 symmetry<br>Appears flipped across one of three diagonal lines during (period/2)<br>Lines intersect at a vertex
	\|		\| 3 diagonals<br>p/2
	\|-		\|-
	! C3_3		! C3_3
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	\| 2		\| 2
	\| Pattern has C3_3 symmetry<br>Appears flipped across one of three diagonal lines during (period/2)<br>Lines intersect at the center of a cell		\| Pattern has C3_3 symmetry<br>Appears flipped across one of three diagonal lines during (period/2)<br>Lines intersect at the center of a cell
	\|		\| 3 diagonals<br>p/2
	\|-		\|-
	! D6_1o		! D6_1o
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	\| 2		\| 2
	\| Pattern has D6_1o symmetry<br>Appears rotated 60 degrees during (period/2)<br>Could also be interpreted as flipping on one of three diagonal lines<br>Rotation is centered on/lines intersect at a vertex		\| Pattern has D6_1o symmetry<br>Appears rotated 60 degrees during (period/2)<br>Could also be interpreted as flipping on one of three diagonal lines<br>Rotation is centered on/lines intersect at a vertex
	\|		\| 3 diagonals<br>p/2
	\|-		\|-
	! D6_1		! D6_1
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	\| 2		\| 2
	\| Pattern has C6 symmetry<br>Appears flipped across one of three diagonal lines and<br>and one of three orthogonal lines during (period/2)<br>Lines intersect at a vertex		\| Pattern has C6 symmetry<br>Appears flipped across one of three diagonal lines and<br>and one of three orthogonal lines during (period/2)<br>Lines intersect at a vertex
	\|		\| 3 diagonals<br>p/2
	\|}		\|}

Gzaytman: /* Kinetic */

2025-10-13T06:12:36Z

Kinetic

← Older revision		Revision as of 06:12, 13 October 2025
Line 196:		Line 196:
	\| 3		\| 3
	\| Pattern has C2_1 symmetry<br>Appears rotated 60 degrees during (period/3)<br>Rotation is centered on a vertex		\| Pattern has C2_1 symmetry<br>Appears rotated 60 degrees during (period/3)<br>Rotation is centered on a vertex
	\|		\| none
	\|-		\|-
	! C2_4		! C2_4
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	\| 2		\| 2
	\| Pattern has C3_1 symmetry<br>Appears rotated 60 degrees during (period/2)<br>Rotation is centered on a vertex		\| Pattern has C3_1 symmetry<br>Appears rotated 60 degrees during (period/2)<br>Rotation is centered on a vertex
	\|		\| none
	\|-		\|-
	! C3_1		! C3_1
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	\| 2		\| 2
	\| Pattern has C3_1 symmetry<br>Appears flipped across one of three orthogonal lines during (period/2)<br>Lines intersect at a vertex		\| Pattern has C3_1 symmetry<br>Appears flipped across one of three orthogonal lines during (period/2)<br>Lines intersect at a vertex
	\|		\| none
	\|-		\|-
	! C3_1		! C3_1

Gzaytman: /* Kinetic */

2025-10-13T06:04:54Z

Kinetic

← Older revision		Revision as of 06:04, 13 October 2025
Line 136:		Line 136:
	\| 2		\| 2
	\| Pattern is asymmetric<br>Appears rotated 180 degrees during (period/2)<br>Rotation is centered on a vertex		\| Pattern is asymmetric<br>Appears rotated 180 degrees during (period/2)<br>Rotation is centered on a vertex
	\|		\| none
	\|-		\|-
	! C1		! C1
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	\| 2		\| 2
	\| Pattern is asymmetric<br>Appears rotated 180 degrees during (period/2)<br>Rotation is centered on an edge		\| Pattern is asymmetric<br>Appears rotated 180 degrees during (period/2)<br>Rotation is centered on an edge
	\|		\| none
	\|-		\|-
	! C1		! C1

Muzik: /* Kinetic */

2025-10-12T17:52:24Z

Kinetic

← Older revision		Revision as of 17:52, 12 October 2025
Line 238:		Line 238:
	\| 2		\| 2
	\| Pattern has D6_1 symmetry<br>Appears rotated 60 degrees during (period/2)<br>Could also be interpreted as flipping on one of three orthogonal lines<br>Rotation is centered on/lines intersect at a vertex		\| Pattern has D6_1 symmetry<br>Appears rotated 60 degrees during (period/2)<br>Could also be interpreted as flipping on one of three orthogonal lines<br>Rotation is centered on/lines intersect at a vertex
	\|		\| none
	\|-		\|-
	! C6		! C6

Muzik: /* Kinetic */

2025-10-09T22:35:14Z

Kinetic

← Older revision		Revision as of 22:35, 9 October 2025
Line 123:		Line 123:
	! D2_xo		! D2_xo
	\| 2		\| 2
	\| Pattern is asymmetric<br>Appears flipped across an orthogonal line during (period/2)<br>Line passes through vertices~~, cell centers~~ and ~~edge midpoints~~		\| Pattern is asymmetric<br>Appears flipped across an orthogonal line during (period/2)<br>Line passes through vertices and edges
	\| none		\| none
	\|-		\|-
Line 129:		Line 129:
	! D2_x		! D2_x
	\| 2		\| 2
	\| Pattern is asymmetric<br>Appears flipped across a diagonal line during (period/2)<br>Line passes through vertices and ~~edges~~		\| Pattern is asymmetric<br>Appears flipped across a diagonal line during (period/2)<br>Line passes through vertices, cell centers and edge midpoints
	\| 1 diagonal<br>p/2		\| 1 diagonal<br>p/2
	\|-		\|-

Muzik: /* Kinetic */

2025-10-09T22:34:53Z

Kinetic

← Older revision		Revision as of 22:34, 9 October 2025
Line 123:		Line 123:
	! D2_xo		! D2_xo
	\| 2		\| 2
	\| Pattern is asymmetric<br>Appears flipped across an orthogonal line during (period/2)<br>Line passes through ~~edges only~~		\| Pattern is asymmetric<br>Appears flipped across an orthogonal line during (period/2)<br>Line passes through vertices, cell centers and edge midpoints
	\| none		\| none
	\|-		\|-
Line 129:		Line 129:
	! D2_x		! D2_x
	\| 2		\| 2
	\| Pattern is asymmetric<br>Appears flipped across a diagonal line during (period/2)<br>Line passes through vertices and ~~cell centers~~		\| Pattern is asymmetric<br>Appears flipped across a diagonal line during (period/2)<br>Line passes through vertices and edges
	\| 1 diagonal<br>p/2		\| 1 diagonal<br>p/2
	\|-		\|-