List of bracketopes (Meta, 4)

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This is a list of bracketopes in dimensions from one to three.

Name	Rotopic index	Bracketopic index	Bracket notation	CSG notation
1D bracketopes
Line	1	1	[x]	E
2D bracketopes
Square	2	2	[xy]	EE
Diamond*	N/A	3	<xy>	ED
Circle	4	4	(xy)	EL
3D bracketopes
Cube	5	5	[xyz]	EEE
Cuboid*	N/A	6	[<xy>z]	EDE
Cylinder	11	7	[(xy)z]	ELE
Wide octahedron*	N/A	8	<[xy]z>	EED
Octahedron	N/A	9	<xyz>	EDD
Bicone	N/A	10	<(xy)z>	ELD
Crind	N/A	11	([xy]z)	ELE&EEL
Narrow crind*	N/A	12	(<xy>z)	(ELE&EEL)R_x[45°]S_yz[2^-1√2]
Sphere	7	13	(xyz)	ELL
4D bracketopes
Tesseract	45	14	[xyzw]	EEEE
Narrow tesseract*	N/A	15	[<xy>zw]	EDEE
Cubinder	34	16	[(xy)zw]	ELEE
Wide octahedral prism*	N/A	17	[<[xy]z>w]	EEDE
Octahedral prism	N/A	18	[<xyz>w]	EDDE
Biconic prism	N/A	19	[<(xy)z>w]	ELDE
Crindal prism	N/A	20	[([xy]z)w]	(EL&LE)E
Narrow crindal prism*	N/A	21	[(<xy>z)w]	(ELE&EEL)R_x[45°]S_yz[2^-1√2]E
Spherinder	20	22	[(xyz)w]	ELLE <[xyz]w> bicubone? <[<xy>z]w> narrow bicubone* <[(xy)z]w> bicylone <[xy]zw> wide hexadecachoron* <xyzw> hexadecachoron <(xy)zw> dibicone <([xy]z)w> bicrone <(<xy>z)w> narrow bicrone* <(xyz)w> bisphone
Cubic bipyramid?	N/A	23	<[xyz]w>	EEED
Narrow cubic bipyramid*	N/A	24	<[<xy>z]w>	EDED
Cylindrical bipyramid	N/A	25	<[(xy)z]w>	ELE
Wide hexadecachoron*	N/A	26	<[xy]zw>	EEDD
Hexadecachoron	N/A	27	<xyzw>	EDDD
Dibicone	N/A	28	<(xy)zw>	ELDD
Crindal bipyramid	N/A	29	<([xy]z)w>	(ELE&EEL)D
Narrow crindal bipyramid*	N/A	30	<(<xy>z)w>	(ELE&EEL)R_x[45°]S_yz[2^-1√2]D
Bisphone	N/A	31	<(xyz)w>	ELLD