Perovskite is a crystal structure with a simple cubic Bravais lattice and five atoms in the basis. The cubic form is typically the high temperature phase of perovskite compounds. They often go through a structural phase transition to a tetragonal phase or some other phase with lower symmetry. Perovskites are often ferroelectrics, piezoelectrics, and pyroelectrics. They can have very high dielectric constants and are used in supercapacitors. There are perovskite superconductors and they have promising applications in solar cells.

Crystal structure: Perovskite
Bravais lattice: Simple cubic
Space group: 221 ($Pm\overline{3}m$),   Strukturbericht: E2₁,   Pearson symbol: cP5
Point group: m3m (O_h)   six 2-fold rotations, four 3-fold rotations, three 4-fold rotations, nine mirror planes, inversion

The lattice parameters of the conventional unit cell are:

\[ \begin{equation} a = b = c, \hspace{0.5cm} \alpha = 90^{\circ} , \,\beta = 90^{\circ} ,\,\gamma = 90^{\circ} . \end{equation} \]

The primitive unit cell is the same as the conventional unit cell. The primitive lattice vectors are,

$\vec{a}_1=a\hat{x}$,   $\vec{a}_2=a\hat{y}$,   $\vec{a}_3=a\hat{z}$.

There are three atoms in asymmetric unit,

Ca (0,0,0), Ti (0.5,0.5,0.5), O (0.5,0.5,0),

and five atoms in the basis,

Ca (0,0,0), Ti (0.5,0.5,0.5), O (0.5,0.5,0), O (0.5,0,0.5), O (0,0.5,0.5).

Space group: 221 ($Pm\overline{3}m$)
48 symmetry operations:

1	x,y,z	identity
2	-x,-y,z	C2 axis
3	-x,y,-z	C2 axis
4	x,-y,-z	C2 axis
5	z,x,y	C3 axis
6	z,-x,-y	C3 axis
7	-z,-x,y	C3 axis
8	-z,x,-y	C3 axis
9	y,z,x	C3 axis
10	-y,z,-x	C3 axis
11	y,-z,-x	C3 axis
12	-y,-z,x	C3 axis
13	y,x,-z	C2 axis
14	-y,-x,-z	C2 axis
15	y,-x,z	C4 axis
16	-y,x,z	C4 axis
17	x,z,-y	C4 axis
18	-x,z,y	C2 axis
19	-x,-z,-y	C2 axis
20	x,-z,y	C4 axis
21	z,y,-x	C4 axis
22	z,-y,x	C2 axis
23	-z,y,x	C4 axis
24	-z,-y,-x	C2 axis
25	-x,-y,-z	Ci: 0 0 0
26	x,y,-z	mirror plane
27	x,-y,z	mirror plane
28	-x,y,z	mirror plane
29	-z,-x,-y	3-bar axis|inversion center at 0 0 0
30	-z,x,y	3-bar axis|inversion center at 0 0 0
31	z,x,-y	3-bar axis|inversion center at 0 0 0
32	z,-x,y	3-bar axis|inversion center at 0 0 0
33	-y,-z,-x	3-bar axis|inversion center at 0 0 0
34	y,-z,x	3-bar axis|inversion center at 0 0 0
35	-y,z,x	3-bar axis|inversion center at 0 0 0
36	y,z,-x	3-bar axis|inversion center at 0 0 0
37	-y,-x,z	mirror plane
38	y,x,z	mirror plane
39	-y,x,-z	4-bar axis|inversion center at 0 0 0
40	y,-x,-z	4-bar axis|inversion center at 0 0 0
41	-x,-z,y	4-bar axis|inversion center at 0 0 0
42	x,-z,-y	mirror plane
43	x,z,y	mirror plane
44	-x,z,-y	4-bar axis|inversion center at 0 0 0
45	-z,-y,x	4-bar axis|inversion center at 0 0 0
46	-z,y,-x	mirror plane
47	z,-y,-x	4-bar axis|inversion center at 0 0 0
48	z,y,x	mirror plane