Orbifold Atlas

Underlying Topological Space: S³; Figure Pseudo-Symmetry (FPS): 1
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 432 a

6-1 J* 422 b

8-1 P₂ 322 c

12-1 W* 222 d

12-1 I6[-]J*2 32<4>22 (e:a-b)¹

16-1 I8[-]P₂2 42<3>22 f:a-c

24-1 J*4[-]W*2 42<2>22 g:b-d

24-1 I12[J₂]J*4 43<2>42 (h:a-b)²

24-2 P₂3[-]W*2 32<2>22 (i1:c-d)³, (i2:c-d)⁴

48 1 j:efghi

48-1 P₂6[-]J₂2 2*=332<1>22 j1:c-h [#207(e)]

48-2 m* (j2:geh)⁵, (j3:feh)⁶ #229(j,k)

Struct-Mult Critical Points Heegaard Surf Wyckoff Cut

BCC -1 I/P₂/W*/J* H42{22} e i2 h i1

Lattice Points: (1) 0,0,0 + (1/2,0,0); (2) 0,0,0 + (1/2,1/2,0); (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) x,x,z

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FPS	Mult	Lattice Comp	Group Graph	Wyckoff Set	2[4]Cover
	2-1	I	432	a
	6-1	J*	422	b
	8-1	P₂	322	c
	12-1	W*	222	d
	12-1	I6[-]J*2	32<4>22	(e:a-b)¹
	16-1	I8[-]P₂2	42<3>22	f:a-c
	24-1	J4[-]W2	42<2>22	g:b-d
	24-1	I12[J₂]J*4	43<2>42	(h:a-b)²
	24-2	P₂3[-]W*2	32<2>22	(i1:c-d)³, (i2:c-d)⁴
	48		1	j:efghi
	48-1	P₂6[-]J₂2	2*=332<1>22	j1:c-h	[#207(e)]
	48-2		m*	(j2:geh)⁵, (j3:feh)⁶	#229(j,k)

Struct-Mult	Critical Points	Heegaard Surf	Wyckoff Cut
BCC -1	I/P₂/W/J	H42{22}	e i2 h i1