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

1-2 P 432 a, b

3-2 J 422 c, d

6-2 P6[-]J2 32<4>22 e:a-d, f:b-c

8-1 P8[P₂]P8 42<3>42 (g:a-b)¹

12-1 J4[W*]J4 42<2>42 (h:d-c)²

12-2 P12[-]J4 43<2>42 i:a-c, j:b-d

24 1 k:efghij

2 24-2 P₂3[-]W*2 2*=33<1>22 (k1:g-h)³, (k2:g-h)⁴ #211(i)

24-2 m* (k3:hie)⁵, (k4:hfj)⁶ #221(k,l)

24-1 m* (k5:gfiej)⁷ #221(m)

Struct-Mult Critical Points Heegaard Surf Wyckoff Cut

Scub-1s P/J/J/P H322{2} g j h i

CsCl-1 PP/P₂/W*/JJ H4242{11} e i f j

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

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FPS	Mult	Lattice Comp	Group Graph	Wyckoff Set	2[4]Cover
	1-2	P	432	a, b
	3-2	J	422	c, d
	6-2	P6[-]J2	32<4>22	e:a-d, f:b-c
	8-1	P8[P₂]P8	42<3>42	(g:a-b)¹
	12-1	J4[W*]J4	42<2>42	(h:d-c)²
	12-2	P12[-]J4	43<2>42	i:a-c, j:b-d
	24		1	k:efghij
2	24-2	P₂3[-]W*2	2*=33<1>22	(k1:g-h)³, (k2:g-h)⁴	#211(i)
	24-2		m*	(k3:hie)⁵, (k4:hfj)⁶	#221(k,l)
	24-1		m*	(k5:gfiej)⁷	#221(m)

Struct-Mult	Critical Points	Heegaard Surf	Wyckoff Cut
Scub-1s	P/J/J/P	H322{2}	g j h i
CsCl-1	PP/P₂/W*/JJ	H4242{11}	e i f j