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Cubic Close Packing

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Common name

fcc

Description of lattice

basis | (-1 | -1 | 0) | (1 | -1 | 0) | (0 | 1 | -1)
Gram matrix | (2 | 0 | -1
0 | 2 | -1
-1 | -1 | 2)

Lattice invariants

dimension | 3
determinant | 4
minimal squared norm | 2
kissing number | 12

Lattice-packing invariants

Quadratic form and theta series

quadratic form | 2 x^2 - 2 x z + 2 y^2 - 2 y z + 2 z^2
theta series (closed series) | 1/2 (ϑ_3(0, e^(i π x))^3 + ϑ_4(0, e^(i π x))^3)

More properties

number of symmetries | 48

Common properties

even | integral | nonunimodular

Crystallographic properties

Point groups

crystal class | Schönflies | Hermann-Mauguin
tetartoidal | T | 23
diploidal | T_h | m3^_
gyroidal | O | 432
tetrahedral | T_d | 4^_3m
hexoctahedral | O_h | m3^_m

Space groups

crystal class | IUCr number | Hermann-Mauguin
tetartoidal | 195 | F23
diploidal | 200 | 201 | Fd3^_ | Fm3^_
gyroidal | 207 | 208 | F4132 | F432
tetrahedral | 215 | 216 | F43c^_ | F43m^_
hexoctahedral | 221 | 222 | 223 | 224 | Fd3c^_ | Fd3m^_ | Fm3c^_ | Fm3m^_

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