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Symmetry Groups (Point group — Origami)


Shapes corresponding to different point groups

D2h
D2
D2d
C2v
C1
Cs
C2
Ci
↓turn up
turn down↑
C2h
S4
D3h
D3
D3d
C3v
C3
C3h
S6

Broken lines indicate folds.

Folding directions are the same except Ci .

Cn , Dn , Cnv , Cnh , Dnh , Dnd and S2n can be made using the same logic.

T , Td , Th , O , Oh and Ih can be made joining four C3 , four D3v , six C2v , eight C3 , eight D3v and twenty D3v cards, respectively.

Linkage of six C2v cards can also form a Td shape.

Th can be also made joining four C3 cards plus four mirror-image C3 cards.

four rings six rings

Twine of three rings forms Th .

Twine of four rings forms O .

Twine of six rings forms I .
→ Let's make origami cane-ball!

Twine of ten rings also forms I .
→ Let's make origami cane-ball!


Polyhedron

ten rings

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