Cyclic colourings and polar space groups

◦ 0 lifts

Base group: ◦ P1

2222 2 lifts

Static perfect 2-colouring for group g6: asymmetric motifs carry phase colours for Conway type 2222/◦.

P2₁

UCL space-group page

Base group: 2222 P2

Presentation

Geometric generators modulo full-cell translations for space group P2₁
A	Half-turn (180°) screw rotation about an axis parallel to the lift direction; height shift 1/2

Relations G/Λ = ⟨A | A² = 1⟩

Static perfect 2-colouring for group g7: asymmetric motifs carry phase colours for Conway type 2222/2222.

C2

UCL space-group page

Base group: 2222 P2

Presentation

Geometric generators modulo full-cell translations for space group C2
A	Translation by 1/2 b + 1/2 c
B	Half-turn (180°) rotation about an axis parallel to the lift direction

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

∗∗ 0 lifts

Base group: ∗∗ Pm

×× 0 lifts

Base group: ×× Pc

∗× 1 lift

Static perfect 2-colouring for group g9: asymmetric motifs carry phase colours for Conway type *×/◦.

Cc

UCL space-group page

Base group: ∗× Cm

Presentation

Geometric generators modulo full-cell translations for space group Cc
A	Glide reflection in a vertical plane; height shift 1/2

Relations G/Λ = ⟨A | A² = 1⟩

∗2222 5 lifts

Static perfect 2-colouring for group g55: asymmetric motifs carry phase colours for Conway type *2222/2222.

Pcc2

UCL space-group page

Base group: ∗2222 Pmm2

Presentation

Geometric generators modulo full-cell translations for space group Pcc2
A	Glide reflection in a vertical plane, direction 1; height shift 1/2
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

Static perfect 2-colouring for group g60: asymmetric motifs carry phase colours for Conway type *2222/**.

Pmc2₁

UCL space-group page

Base group: ∗2222 Pmm2

Presentation

Geometric generators modulo full-cell translations for space group Pmc2₁
A	Mirror reflection in a vertical plane, direction 1
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

Static perfect 2-colouring for group g64: asymmetric motifs carry phase colours for Conway type *2222/*2222.

Amm2

UCL space-group page

Base group: ∗2222 Pmm2

Presentation

Geometric generators modulo full-cell translations for space group Amm2
A	Translation by 1/2 b + 1/2 c
B	Mirror reflection in a vertical plane, direction 1
C	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

Static perfect 2-colouring for group g65: asymmetric motifs carry phase colours for Conway type *2222/22*.

Aem2

UCL space-group page

Base group: ∗2222 Pmm2

Presentation

Geometric generators modulo full-cell translations for space group Aem2
A	Translation by 1/2 b + 1/2 c
B	Glide reflection in a vertical plane, direction 1; height shift 1/2
C	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

Static perfect 2-colouring for group g74: asymmetric motifs carry phase colours for Conway type *2222/2*22.

Fmm2

UCL space-group page

Base group: ∗2222 Pmm2

Presentation

Geometric generators modulo full-cell translations for space group Fmm2
A	Translation by 1/2 b + 1/2 c
B	Translation by 1/2 a + 1/2 c
C	Mirror reflection in a vertical plane, direction 1
D	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B, C, D | A² = B² = C² = D² = 1; AB = BA, AC = CA, AD = DA, BC = CB, BD = DB, CD = DC⟩

22∗ 5 lifts

Static perfect 2-colouring for group g57: asymmetric motifs carry phase colours for Conway type 22*/2222.

Pnc2

UCL space-group page

Base group: 22∗ Pma2

Presentation

Geometric generators modulo full-cell translations for space group Pnc2
A	Glide reflection in a vertical plane; height shift 1/2
B	Half-turn (180°) rotation about an axis parallel to the lift direction

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

Static perfect 2-colouring for group g61: asymmetric motifs carry phase colours for Conway type 22*/××.

Pca2₁

UCL space-group page

Base group: 22∗ Pma2

Presentation

Geometric generators modulo full-cell translations for space group Pca2₁
A	Glide reflection in a vertical plane; height shift 1/2
B	Half-turn (180°) screw rotation about an axis parallel to the lift direction; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

Static perfect 2-colouring for group g62: asymmetric motifs carry phase colours for Conway type 22*/**.

Pmn2₁

UCL space-group page

Base group: 22∗ Pma2

Presentation

Geometric generators modulo full-cell translations for space group Pmn2₁
A	Mirror reflection in a vertical plane
B	Half-turn (180°) screw rotation about an axis parallel to the lift direction; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

Static perfect 2-colouring for group g66: asymmetric motifs carry phase colours for Conway type 22*/22*.

Ama2

UCL space-group page

Base group: 22∗ Pma2

Presentation

Geometric generators modulo full-cell translations for space group Ama2
A	Translation by 1/2 b + 1/2 c
B	Mirror reflection in a vertical plane
C	Half-turn (180°) rotation about an axis parallel to the lift direction

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

Static perfect 2-colouring for group g67: asymmetric motifs carry phase colours for Conway type 22*/22×.

Aea2

UCL space-group page

Base group: 22∗ Pma2

Presentation

Geometric generators modulo full-cell translations for space group Aea2
A	Translation by 1/2 b + 1/2 c
B	Glide reflection in a vertical plane; height shift 1/2
C	Half-turn (180°) rotation about an axis parallel to the lift direction

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

22× 3 lifts

Static perfect 2-colouring for group g59: asymmetric motifs carry phase colours for Conway type 22×/2222.

Pnn2

UCL space-group page

Base group: 22× Pba2

Presentation

Geometric generators modulo full-cell translations for space group Pnn2
A	Half-turn (180°) rotation about an axis parallel to the lift direction
B	Glide reflection in a vertical plane; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

Static perfect 2-colouring for group g63: asymmetric motifs carry phase colours for Conway type 22×/××.

Pna2₁

UCL space-group page

Base group: 22× Pba2

Presentation

Geometric generators modulo full-cell translations for space group Pna2₁
A	Half-turn (180°) screw rotation about an axis parallel to the lift direction; height shift 1/2
B	Glide reflection in a vertical plane

Relations G/Λ = ⟨A, B | A² = B² = 1; AB = BA⟩

Static perfect 4-colouring for group g75: asymmetric motifs carry phase colours for Conway type 22×⁴/2222.

Fdd2

UCL space-group page

Base group: 22× Pba2

Presentation

Geometric generators modulo full-cell translations for space group Fdd2
A	Half-turn (180°) screw rotation about an axis parallel to the lift direction; height shift 1/2
B	Glide reflection in a vertical plane; height shift 3/4

Relations G/Λ = ⟨A, B | A² = B⁴ = (AB)⁴ = 1; AB² = B²A⟩

2∗22 5 lifts

Static perfect 2-colouring for group g69: asymmetric motifs carry phase colours for Conway type 2*22/2222.

Ccc2

UCL space-group page

Base group: 2∗22 Cmm2

Presentation

Geometric generators modulo full-cell translations for space group Ccc2
A	Translation by 1/2 a + 1/2 b
B	Glide reflection in a vertical plane, direction 1; height shift 1/2
C	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

Static perfect 2-colouring for group g70: asymmetric motifs carry phase colours for Conway type 2*22/*×.

Cmc2₁

UCL space-group page

Base group: 2∗22 Cmm2

Presentation

Geometric generators modulo full-cell translations for space group Cmc2₁
A	Translation by 1/2 a + 1/2 b
B	Mirror reflection in a vertical plane, direction 1
C	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

Static perfect 2-colouring for group g71: asymmetric motifs carry phase colours for Conway type 2*22/*2222.

Imm2

UCL space-group page

Base group: 2∗22 Cmm2

Presentation

Geometric generators modulo full-cell translations for space group Imm2
A	Translation by 1/2 a + 1/2 b + 1/2 c
B	Mirror reflection in a vertical plane, direction 1
C	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

Static perfect 2-colouring for group g72: asymmetric motifs carry phase colours for Conway type 2*22/22×.

Iba2

UCL space-group page

Base group: 2∗22 Cmm2

Presentation

Geometric generators modulo full-cell translations for space group Iba2
A	Translation by 1/2 a + 1/2 b + 1/2 c
B	Glide reflection in a vertical plane, direction 1; height shift 1/2
C	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

Static perfect 2-colouring for group g73: asymmetric motifs carry phase colours for Conway type 2*22/22*.

Ima2

UCL space-group page

Base group: 2∗22 Cmm2

Presentation

Geometric generators modulo full-cell translations for space group Ima2
A	Translation by 1/2 a + 1/2 b + 1/2 c
B	Glide reflection in a vertical plane, direction 1; height shift 1/2
C	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = 1; AB = BA, AC = CA, BC = CB⟩

442 5 lifts

Static perfect 2-colouring for group g95: asymmetric motifs carry phase colours for Conway type 442/2222.

P4₂

UCL space-group page

Base group: 442 P4

Presentation

Geometric generators modulo full-cell translations for space group P4₂
A	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 1/2

Relations G/Λ = ⟨A | A⁴ = 1⟩

Static perfect 4-colouring for group g96: asymmetric motifs carry phase colours for Conway type 442⁴/◦.

P4₁

UCL space-group page

Base group: 442 P4

Presentation

Geometric generators modulo full-cell translations for space group P4₁
A	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 1/4

Relations G/Λ = ⟨A | A⁴ = 1⟩

Static perfect 4-colouring for group g97: asymmetric motifs carry phase colours for Conway type 442⁴/◦.

P4₃

UCL space-group page

Base group: 442 P4

Presentation

Geometric generators modulo full-cell translations for space group P4₃
A	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 3/4

Relations G/Λ = ⟨A | A⁴ = 1⟩

Static perfect 2-colouring for group g98: asymmetric motifs carry phase colours for Conway type 442/442.

I4

UCL space-group page

Base group: 442 P4

Presentation

Geometric generators modulo full-cell translations for space group I4
A	Translation by 1/2 a + 1/2 b + 1/2 c
B	1/4-turn (90°) rotation about an axis parallel to the lift direction

Relations G/Λ = ⟨A, B | A² = B⁴ = 1; AB = BA⟩

Static perfect 4-colouring for group g99: asymmetric motifs carry phase colours for Conway type 442⁴/2222.

I4₁

UCL space-group page

Base group: 442 P4

Presentation

Geometric generators modulo full-cell translations for space group I4₁
A	Translation by 1/2 a + 1/2 b + 1/2 c
B	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 3/4

Relations G/Λ = ⟨A, B | A² = B⁴ = 1; AB = BA⟩

∗442 5 lifts

Static perfect 2-colouring for group g129: asymmetric motifs carry phase colours for Conway type *442/*2222.

P4₂mc

UCL space-group page

Base group: ∗442 P4mm

Presentation

Geometric generators modulo full-cell translations for space group P4₂mc
A	Mirror reflection in a vertical plane, direction 1
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = (AB)⁴ = 1⟩

Static perfect 2-colouring for group g130: asymmetric motifs carry phase colours for Conway type *442/2*22.

P4₂cm

UCL space-group page

Base group: ∗442 P4mm

Presentation

Geometric generators modulo full-cell translations for space group P4₂cm
A	Glide reflection in a vertical plane, direction 1; height shift 1/2
B	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B | A² = B² = (AB)⁴ = 1⟩

Static perfect 2-colouring for group g131: asymmetric motifs carry phase colours for Conway type *442/442.

P4cc

UCL space-group page

Base group: ∗442 P4mm

Presentation

Geometric generators modulo full-cell translations for space group P4cc
A	Glide reflection in a vertical plane, direction 1; height shift 1/2
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = (AB)⁴ = 1⟩

Static perfect 2-colouring for group g136: asymmetric motifs carry phase colours for Conway type *442/*442.

I4mm

UCL space-group page

Base group: ∗442 P4mm

Presentation

Geometric generators modulo full-cell translations for space group I4mm
A	Translation by 1/2 a + 1/2 b + 1/2 c
B	Mirror reflection in a vertical plane, direction 1
C	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = (BC)⁴ = 1; AB = BA, AC = CA⟩

Static perfect 2-colouring for group g138: asymmetric motifs carry phase colours for Conway type *442/4*2.

I4cm

UCL space-group page

Base group: ∗442 P4mm

Presentation

Geometric generators modulo full-cell translations for space group I4cm
A	Translation by 1/2 a + 1/2 b + 1/2 c
B	Glide reflection in a vertical plane, direction 1; height shift 1/2
C	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B, C | A² = B² = C² = (BC)⁴ = 1; AB = BA, AC = CA⟩

4∗2 5 lifts

Static perfect 2-colouring for group g133: asymmetric motifs carry phase colours for Conway type 4*2/22×.

P4₂bc

UCL space-group page

Base group: 4∗2 P4bm

Presentation

Geometric generators modulo full-cell translations for space group P4₂bc
A	Glide reflection in a vertical plane; height shift 1/2
B	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B⁴ = (AB)² = 1⟩

Static perfect 2-colouring for group g134: asymmetric motifs carry phase colours for Conway type 4*2/2*22.

P4₂nm

UCL space-group page

Base group: 4∗2 P4bm

Presentation

Geometric generators modulo full-cell translations for space group P4₂nm
A	Mirror reflection in a vertical plane
B	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B⁴ = (AB)² = 1⟩

Static perfect 2-colouring for group g135: asymmetric motifs carry phase colours for Conway type 4*2/442.

P4nc

UCL space-group page

Base group: 4∗2 P4bm

Presentation

Geometric generators modulo full-cell translations for space group P4nc
A	Glide reflection in a vertical plane; height shift 1/2
B	1/4-turn (90°) rotation about an axis parallel to the lift direction

Relations G/Λ = ⟨A, B | A² = B⁴ = (AB)² = 1⟩

Static perfect 4-colouring for group g137: asymmetric motifs carry phase colours for Conway type 4*2⁴/*2222.

I4₁md

UCL space-group page

Base group: 4∗2 P4bm

Presentation

Geometric generators modulo full-cell translations for space group I4₁md
A	Mirror reflection in a vertical plane
B	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 3/4

Relations G/Λ = ⟨A, B | A² = B⁴ = (AB)⁴ = 1; AB² = B²A⟩

Static perfect 4-colouring for group g139: asymmetric motifs carry phase colours for Conway type 4*2⁴/22×.

I4₁cd

UCL space-group page

Base group: 4∗2 P4bm

Presentation

Geometric generators modulo full-cell translations for space group I4₁cd
A	Glide reflection in a vertical plane; height shift 1/2
B	1/4-turn (90°) screw rotation about an axis parallel to the lift direction; height shift 1/4

Relations G/Λ = ⟨A, B | A² = B⁴ = (AB)⁴ = 1; AB² = B²A⟩

333 3 lifts

Static perfect 3-colouring for group g225: asymmetric motifs carry phase colours for Conway type 333³/◦.

P3₂

UCL space-group page

Base group: 333 P3

Presentation

Geometric generators modulo full-cell translations for space group P3₂
A	1/3-turn (120°) screw rotation about an axis parallel to the lift direction; height shift 1/3

Relations G/Λ = ⟨A | A³ = 1⟩

Static perfect 3-colouring for group g226: asymmetric motifs carry phase colours for Conway type 333³/◦.

P3₁

UCL space-group page

Base group: 333 P3

Presentation

Geometric generators modulo full-cell translations for space group P3₁
A	1/3-turn (120°) screw rotation about an axis parallel to the lift direction; height shift 2/3

Relations G/Λ = ⟨A | A³ = 1⟩

Static perfect 3-colouring for group g227: asymmetric motifs carry phase colours for Conway type 333³/333.

R3

UCL space-group page

Base group: 333 P3

Presentation

Geometric generators modulo full-cell translations for space group R3
A	Translation by 1/3 a − 1/3 b + 2/3 c
B	1/3-turn (120°) rotation about an axis parallel to the lift direction

Relations G/Λ = ⟨A, B | A³ = B³ = 1; AB = BA⟩

∗333 1 lift

Static perfect 2-colouring for group g231: asymmetric motifs carry phase colours for Conway type *333/333.

P3c1

UCL space-group page

Base group: ∗333 P3m1

Presentation

Geometric generators modulo full-cell translations for space group P3c1
A	Glide reflection in a vertical plane, direction 1; height shift 1/2
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = (AB)³ = 1⟩

3∗3 3 lifts

Static perfect 2-colouring for group g233: asymmetric motifs carry phase colours for Conway type 3*3/333.

P31c

UCL space-group page

Base group: 3∗3 P31m

Presentation

Geometric generators modulo full-cell translations for space group P31c
A	Glide reflection in a vertical plane, direction 1; height shift 1/2
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = (AB)³ = 1⟩

Static perfect 3-colouring for group g234: asymmetric motifs carry phase colours for Conway type 3*3³/*333.

R3m

UCL space-group page

Base group: 3∗3 P31m

Presentation

Geometric generators modulo full-cell translations for space group R3m
A	Mirror reflection in a vertical plane
B	1/3-turn (120°) screw rotation about an axis parallel to the lift direction; height shift 2/3

Relations G/Λ = ⟨A, B | A² = B³ = 1; B(ABA) = (ABA)B⟩

Static perfect 6-colouring for group g235: asymmetric motifs carry phase colours for Conway type 3*3⁶/333.

R3c

UCL space-group page

Base group: 3∗3 P31m

Presentation

Geometric generators modulo full-cell translations for space group R3c
A	Glide reflection in a vertical plane; height shift 1/2
B	1/3-turn (120°) screw rotation about an axis parallel to the lift direction; height shift 2/3

Relations G/Λ = ⟨A, B | A² = B³ = 1; B(ABA) = (ABA)B⟩

632 5 lifts

Static perfect 3-colouring for group g244: asymmetric motifs carry phase colours for Conway type 632³/2222.

P6₂

UCL space-group page

Base group: 632 P6

Presentation

Geometric generators modulo full-cell translations for space group P6₂
A	1/6-turn (60°) screw rotation about an axis parallel to the lift direction; height shift 2/3

Relations G/Λ = ⟨A | A⁶ = 1⟩

Static perfect 3-colouring for group g245: asymmetric motifs carry phase colours for Conway type 632³/2222.

P6₄

UCL space-group page

Base group: 632 P6

Presentation

Geometric generators modulo full-cell translations for space group P6₄
A	1/6-turn (60°) screw rotation about an axis parallel to the lift direction; height shift 1/3

Relations G/Λ = ⟨A | A⁶ = 1⟩

Static perfect 2-colouring for group g246: asymmetric motifs carry phase colours for Conway type 632/333.

P6₃

UCL space-group page

Base group: 632 P6

Presentation

Geometric generators modulo full-cell translations for space group P6₃
A	1/6-turn (60°) screw rotation about an axis parallel to the lift direction; height shift 1/2

Relations G/Λ = ⟨A | A⁶ = 1⟩

Static perfect 6-colouring for group g247: asymmetric motifs carry phase colours for Conway type 632⁶/◦.

P6₅

UCL space-group page

Base group: 632 P6

Presentation

Geometric generators modulo full-cell translations for space group P6₅
A	1/6-turn (60°) screw rotation about an axis parallel to the lift direction; height shift 1/6

Relations G/Λ = ⟨A | A⁶ = 1⟩

Static perfect 6-colouring for group g248: asymmetric motifs carry phase colours for Conway type 632⁶/◦.

P6₁

UCL space-group page

Base group: 632 P6

Presentation

Geometric generators modulo full-cell translations for space group P6₁
A	1/6-turn (60°) screw rotation about an axis parallel to the lift direction; height shift 5/6

Relations G/Λ = ⟨A | A⁶ = 1⟩

∗632 3 lifts

Static perfect 2-colouring for group g269: asymmetric motifs carry phase colours for Conway type *632/3*3.

P6₃cm

UCL space-group page

Base group: ∗632 P6mm

Presentation

Geometric generators modulo full-cell translations for space group P6₃cm
A	Mirror reflection in a vertical plane, direction 1
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = (AB)⁶ = 1⟩

Static perfect 2-colouring for group g270: asymmetric motifs carry phase colours for Conway type *632/632.

P6cc

UCL space-group page

Base group: ∗632 P6mm

Presentation

Geometric generators modulo full-cell translations for space group P6cc
A	Glide reflection in a vertical plane, direction 1; height shift 1/2
B	Glide reflection in a vertical plane, direction 2; height shift 1/2

Relations G/Λ = ⟨A, B | A² = B² = (AB)⁶ = 1⟩

Static perfect 2-colouring for group g271: asymmetric motifs carry phase colours for Conway type *632/*333.

P6₃mc

UCL space-group page

Base group: ∗632 P6mm

Presentation

Geometric generators modulo full-cell translations for space group P6₃mc
A	Glide reflection in a vertical plane, direction 1; height shift 1/2
B	Mirror reflection in a vertical plane, direction 2

Relations G/Λ = ⟨A, B | A² = B² = (AB)⁶ = 1⟩

Cyclic colourings ↔ polar space groups

P21

Presentation

C2

Presentation

Cc

Presentation

Pcc2

Presentation

Pmc21

Presentation

Amm2

Presentation

Aem2

Presentation

Fmm2

Presentation

Pnc2

Presentation

Pca21

Presentation

Pmn21

Presentation

Ama2

Presentation

Aea2

Presentation

Pnn2

Presentation

Pna21

Presentation

Fdd2

Presentation

Ccc2

Presentation

Cmc21

Presentation

Imm2

Presentation

Iba2

Presentation

Ima2

Presentation

P42

Presentation

P41

Presentation

P43

Presentation

I4

Presentation

I41

Presentation

P42mc

Presentation

P42cm

Presentation

P4cc

Presentation

I4mm

Presentation

I4cm

Presentation

P42bc

Presentation

P42nm

Presentation

P4nc

Presentation

I41md

Presentation

I41cd

Presentation

P32

Presentation

P31

Presentation

R3

Presentation

P3c1

Cyclic colourings polar space groups

P2₁

Pmc2₁

Pca2₁

Pmn2₁

Pna2₁

Cmc2₁

P4₂

P4₁

P4₃

I4₁

P4₂mc

P4₂cm

P4₂bc

P4₂nm

I4₁md

I4₁cd

P3₂

P3₁

P6₂

P6₄

P6₃

P6₅

P6₁

P6₃cm

P6₃mc