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 332 a, b

3-2 J 222 c, d

4-2 P4[F]P4 32<3>32 (e1:a-b, e2:b-a)¹

6-2 P6[-]J2 33<2>22 f:a-d, i:b-c

6-2 J2[W]J2 22<2>22 (g:d-c)², (h:d-c)³

12 1 j:efghi

12-2 P12[-]J4 2*=332<1>222 j1:a-c, j2:b-d #207(i,j)

2 12-2 F3[-]W2 2*=33<1>22 j3:e1-h, j4:e2-g #208(j,k)

12-2 m* (j5:fgh)⁴, (j6:ghi)⁵ #200(j,k)

12-1 m* (j7:efi)⁶ #215(i)

Struct-Mult Critical Points Heegaard Surf Wyckoff Cut

Scub-1s P/J/J/P H33{22} h e1 g e2

Lattice Points: (1) 0,0,0 + (1/4,1/4,1/4) x4&; (2) 1/2,0,0 + (0,1/4,0) x2; (3) 1/2,0,0 + (0,0,1/4) x2; (4) 0,y,z; (5) 1/2,y,z; (6) x,x,z

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FPS	Mult	Lattice Comp	Group Graph	Wyckoff Set	2[4]Cover
	1-2	P	332	a, b
	3-2	J	222	c, d
	4-2	P4[F]P4	32<3>32	(e1:a-b, e2:b-a)¹
	6-2	P6[-]J2	33<2>22	f:a-d, i:b-c
	6-2	J2[W]J2	22<2>22	(g:d-c)², (h:d-c)³
	12		1	j:efghi
	12-2	P12[-]J4	2*=332<1>222	j1:a-c, j2:b-d	#207(i,j)
2	12-2	F3[-]W2	2*=33<1>22	j3:e1-h, j4:e2-g	#208(j,k)
	12-2		m*	(j5:fgh)⁴, (j6:ghi)⁵	#200(j,k)
	12-1		m*	(j7:efi)⁶	#215(i)

Struct-Mult	Critical Points	Heegaard Surf	Wyckoff Cut
Scub-1s	P/J/J/P	H33{22}	h e1 g e2