Orbifold Atlas

Underlying Topological Space: S³; Figure Pseudo-Symmetry (FPS): 222
Euclidean 3-Orbifold with Invariant-Lattice-Complex Letters (left), Wyckoff Site Letters (right)

FPS Mult Lattice Comp Group Graph Wyckoff Set 2[4]Cover

4-1 [F,+Y,F,-Y,F,+Y,F,-Y]& <3>& (a:)¹

4-4 F 33 a4&a1, a1&a2, a2&a3, a3&a4

4-2 F[+Y]F 3<3>3 a1, a3

4-2 F[-Y]F 3<3>3 a2, a4

12 1 b:a

2 12-1 [+V,S,-V,`S]& 2*=<1>& (b1:)²

2 12-1 +Y3[+V]+Y3 2*=33<1>33 b2:a1-a3 #212(d)

2 12-1 +Y3[-V]+Y3 2*=33<1>33 b3:a1-a3 #212(d)

12-1 -Y3[-V]-Y3 2*=33<1>33 b4:a2-a4 #213(d)

12-1 -Y3[+V]-Y3 2*=33<1>33 b5:a2-a4 #213(d)

Lattice Points: (1) 0,0,0 + (1/8,1/8,1/8) x8 &; (2) 1/8,0,1/4 + (1/4,0,0) x4 &

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FPS	Mult	Lattice Comp	Group Graph	Wyckoff Set	2[4]Cover
	4-1	[F,+Y,F,-Y,F,+Y,F,-Y]&	<3>&	(a:)¹
	4-4	F	33	a4&a1, a1&a2, a2&a3, a3&a4
	4-2	F[+Y]F	3<3>3	a1, a3
	4-2	F[-Y]F	3<3>3	a2, a4
	12		1	b:a
2	12-1	[+V,S,-V,`S]&	2*=<1>&	(b1:)²
2	12-1	+Y3[+V]+Y3	2*=33<1>33	b2:a1-a3	#212(d)
2	12-1	+Y3[-V]+Y3	2*=33<1>33	b3:a1-a3	#212(d)
	12-1	-Y3[-V]-Y3	2*=33<1>33	b4:a2-a4	#213(d)
	12-1	-Y3[+V]-Y3	2*=33<1>33	b5:a2-a4	#213(d)