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

2-1 I 332 a

4-2 F 322 b, c

6-1 J* 222 d

6-2 W 222 e, f

8-2 I4[-]F2 22<3>22 (g1:b-a, g2:a-c)¹

12-1 I6[-]J*2 33<2>22 (h:a-d)²

12-2 W2[-]J*2 22<2>22 (i:d-e)³, (j:d-f)⁴

12-4 F3[-]W2 32<2>22 l1:c-e, l2:c-f, k1:b-e, k2:b-f

24 1 m:ghijkl

2 24-1 I12[J₂]J*4 2*=332<1>222 (m1:a-d)⁵ #211(h)

24-1 F6[J₂]F6 2*=332<1>332 (m2:b-c)⁶ [#209(e)]

24-1 m* (m3:hijm1)⁷ #223(k)

24-1 m* (m4:ghm1)⁸ #224(k)

Struct-Mult Critical Points Heegaard Surf Wyckoff Cut

BCC -1 I/FF/WW/J* H2{2222} k1 k2 h l2 l1 .

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

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FPS	Mult	Lattice Comp	Group Graph	Wyckoff Set	2[4]Cover
	2-1	I	332	a
	4-2	F	322	b, c
	6-1	J*	222	d
	6-2	W	222	e, f
	8-2	I4[-]F2	22<3>22	(g1:b-a, g2:a-c)¹
	12-1	I6[-]J*2	33<2>22	(h:a-d)²
	12-2	W2[-]J*2	22<2>22	(i:d-e)³, (j:d-f)⁴
	12-4	F3[-]W2	32<2>22	l1:c-e, l2:c-f, k1:b-e, k2:b-f
	24		1	m:ghijkl
2	24-1	I12[J₂]J*4	2*=332<1>222	(m1:a-d)⁵	#211(h)
	24-1	F6[J₂]F6	2*=332<1>332	(m2:b-c)⁶	[#209(e)]
	24-1		m*	(m3:hijm1)⁷	#223(k)
	24-1		m*	(m4:ghm1)⁸	#224(k)

Struct-Mult	Critical Points	Heegaard Surf	Wyckoff Cut
BCC -1	I/FF/WW/J*	H2{2222}	k1 k2 h l2 l1	.