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Symmetric patterns formed using three different tetrahexes.

 

Pieces	Ternary & Vertical	Double Bilateral	Horizontal	Vertical	Birotary
123	X	X		X	X
124	X	X			X
125	X
126	X
127	X	X			X
134	X	X		X	X
135	X	X			X
136	X	X			X
137	X	X
145	X	X	X		X
146	X	X		X	X
147	X	X		X	X
156	X	X
157	X	X			X
167	X	X			X
234	X	X		X	X
235	X
236	X
237	X	X		X	X
245	X	X		X	X
246	X	X
247	X	X		X	X
256
257
267
345	X	X		X	X
346	X	X			X
347	X
356	X
357	X	X	X	X	X
367	X	X			X
456
457	X	X	X	X	X
467	X	X			X
567