Table of equivalent static symmetries

Name (Hickerson notation)	Catagolue equivalent	Description	Diagram	Example
n	C1	No symmetry		Eater 1
-c	D2_+1	One line of orthogonal mirror symmetry Line passes through cell centers and edges		Hat
-e	D2_+2	One line of orthogonal mirror symmetry Line passes through cell edges and vertices		Cap and table
/	D2_x	One line of diagonal mirror symmetry		Boat
.c	C2_1	180-degree rotation Rotation is centered on the center of a cell		Long snake
.e	C2_2	180-degree rotation Rotation is centered on the edge of a cell		Aircraft carrier
.k	C2_4	180-degree rotation Rotation is centered on the vertex of a cell		Snake
+c	D4_+1	Two lines of orthogonal mirror symmetry Both lines pass through cell centers and edges		Hat cis-siamese hat
+e	D4_+2	Two lines of orthogonal mirror symmetry One line passes through cell centers and edges One line passes through cell edges and vertices		Beehive
+k	D4_+4	Two lines of orthogonal mirror symmetry Both lines pass through cell edges and vertices		unnamed
xc	D4_x1	Two lines of diagonal mirror symmetry Lines meet at the center of a cell		Ship
xk	D4_x4	Two lines of diagonal mirror symmetry Lines meet at the vertex of a cell		Barge
rc	C4_1	90-degree rotation Rotation is centered on the center of a cell		Spiral
rk	C4_4	90-degree rotation Rotation is centered on the vertex of a cell		unnamed
*c	D8_1	Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell centers and edges		Tub
*k	D8_4	Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell edges and vertices		Block