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abr
names: ABR polyhedron
key words: simple tiling, isohedral tiling
references: Phil. Mag. Letts. 76, 423-426 (1997)
embed type space group volume density genus td10
1b P4(2)/mcm 24.2605 0.5771 15 863

unit cell:
a b c alpha beta gamma
2.5479 2.5479 3.7371 90.0 90.0 90.0


vertices: 3
vertex cn x y z symbolic Wyckoff symmetry order
V1 4 0.0 0.0 0.25 0, 0, 1/4 2 b -4m2 8
V2 4 0.0 0.5 0.25 0, 1/2, 1/4 4 e 222 4
V3 4 0.25 0.25 0.3662 x, x, z 8 o m 2

vertex cs1 cs2 cs3 cs4 cs5 cs6 cs7 cs8 cs9 cs10 cum10 vertex symbol
V1 4 8 18 32 56 82 104 140 194 220 859 4.4.4.4.6.6
V2 4 10 22 36 56 84 108 140 186 218 865 4.4.6.6.8.8
V3 4 10 19 36 56 80 111 144 177 225 863 4.6.4.6.6.8


edges: 3
edge x y z symbolic Wyckoff symmetry
E1 0.125 0.125 0.3081 x, x, z 8 o m
E2 0.125 0.375 0.3081 x, y, z 16 p 1
E3 0.25 0.25 0.5 x, x, 1/2 4 j mm2

tiling:
tiling dual vertices edges faces tiles D-symbol
[4^8.6^6.8^2] - 3 3 4 1 21

Export 3dt input: abr-3dt.cgd

Export Systre input: abr.cgd