Orbifold Atlas

Underlying Topological Space: S³; Figure Pseudo-Symmetry (FPS): 2
Euclidean 3-Orbifold with Invariant-Lattice-Complex Letters (left), Wyckoff Site Letters (right)

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

8-1 [P₂,+Y*,P₂,-Y*]& <3>& (a:)¹

8-1 P₂[+Y*]P₂ 3<3>3 a1:

8-1 P₂[-Y*]P₂ 3<3>3 a2:

12-1 [+V,S,-V,'S]& <2>& (b:)²

12-1 'S[+V]S 2<2>2 b1:

12-1 S[-V]'S 2<2>2 b2:

24 1 c:ab

2 24-1 +Y*3[-]+V2 2*=33<1>22 c1:a1-b1 #214(h)

24-1 +Y*3[-]-V2 2*=33<1>22 c2:a1-b2 #214(h)

2 24-1 -Y*3[-]+V2 2*=33<1>22 c3:a2-b1 #214(g)

2 24-1 -Y*3[-]-V2 2*=33<1>22 c4:a2-b2 #214(g)

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

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FPS	Mult	Lattice Comp	Group Graph	Wyckoff Set	2[4]Cover
	8-1	[P₂,+Y,P₂,-Y]&	<3>&	(a:)¹
	8-1	P₂[+Y*]P₂	3<3>3	a1:
	8-1	P₂[-Y*]P₂	3<3>3	a2:
	12-1	[+V,S,-V,'S]&	<2>&	(b:)²
	12-1	'S[+V]S	2<2>2	b1:
	12-1	S[-V]'S	2<2>2	b2:
	24		1	c:ab
2	24-1	+Y*3[-]+V2	2*=33<1>22	c1:a1-b1	#214(h)
	24-1	+Y*3[-]-V2	2*=33<1>22	c2:a1-b2	#214(h)
2	24-1	-Y*3[-]+V2	2*=33<1>22	c3:a2-b1	#214(g)
2	24-1	-Y*3[-]-V2	2*=33<1>22	c4:a2-b2	#214(g)