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

4-4 F 332 a, b, c, d

16-4 F4[T]F4 32<3>32 (e1:a-c, e2:c-b, e3:b-d, e4:d-a)¹

24-2 F6[J₂]F6 33<2>33 f:(a-b)², (g:c-d)³

48 1 h:efg

2 48-2 J₂2[W₂]J₂2 2*=22<1>22 (h1:f-g)⁴, (h2:f-g)⁵ #195(g,h)

48-4 F12[-]J₂2 2*=332<1>22 h3:a-g, h4:b-g, h5:c-f, h6:d-f #209(g,h)

2,2 48-4 T3[W₂]T3 2*=33<1>33 h 7:e1-e3, h8:e2-e4, h9:e3-e1, h10:e4-e2 #210(g)

48-2 m* (h11:gh1)⁶, (h12:fh1)⁷ #202(h)

48-4 m* (h13:efg)⁸ #216(h)

Struct-Mult Critical Points Heegaard Surf Wyckoff Cut

ZnS -2s FF/T/T/FF H3232{11} e4 g e2 f; g e3 f e1

NaCl-1s FF/J₂/J₂/FF H3333{1} e1 e2 e3 e4

FCC -4 FFF/TT/J₂/F H33222{11} e1 e2 g(f1)(f2); (etc. x4)

Lattice Points: (1) 0,0,0 + (1/8,1/8,1/8) x8 &; (2) 0,0,0 + (1/4,0,0) x2; (3) -1/4,1/4,1/4 + (1/4,0,0) x2; (4) 1/4,0,0 + (0,1/8,0) x2; (5) 0,0,1/4 + (0,1/8,0) x2; (6) 0,y,z; (7) 1/4,y,z; (8) x,x,z

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FPS	Mult	Lattice Comp	Group Graph	Wyckoff Set	2[4]Cover
	4-4	F	332	a, b, c, d
	16-4	F4[T]F4	32<3>32	(e1:a-c, e2:c-b, e3:b-d, e4:d-a)¹
	24-2	F6[J₂]F6	33<2>33	f:(a-b)², (g:c-d)³
	48		1	h:efg
2	48-2	J₂2[W₂]J₂2	2*=22<1>22	(h1:f-g)⁴, (h2:f-g)⁵	#195(g,h)
	48-4	F12[-]J₂2	2*=332<1>22	h3:a-g, h4:b-g, h5:c-f, h6:d-f	#209(g,h)
2,2	48-4	T3[W₂]T3	2*=33<1>33	h 7:e1-e3, h8:e2-e4, h9:e3-e1, h10:e4-e2	#210(g)
	48-2		m*	(h11:gh1)⁶, (h12:fh1)⁷	#202(h)
	48-4		m*	(h13:efg)⁸	#216(h)

Struct-Mult	Critical Points	Heegaard Surf	Wyckoff Cut
ZnS -2s	FF/T/T/FF	H3232{11}	e4 g e2 f; g e3 f e1
NaCl-1s	FF/J₂/J₂/FF	H3333{1}	e1 e2 e3 e4
FCC -4	FFF/TT/J₂/F	H33222{11}	e1 e2 g(f1)(f2); (etc. x4)