Table 1.

Construction rules for designing nanohedral protein materials from dimeric and trimeric oligomerization domains

Symmetry*	Construction	Geometry of symmetry elements†
Cages and shells
T‡	Dimer-trimer	54.7°	I
O§	Dimer-trimer	35.3°	I
I	Dimer-trimer	20.9°	I
Double-layer rings
Dn	Dimer-dimer	180°/n	I
Two-dimensional layers
p6¶	Dimer-trimer	0°	N
p321	Dimer-trimer	90°	N
p3	Trimer-trimer	0°	N
Three-dimensional crystals
I213	Dimer-trimer	54.7°	N
P4132 or P4332	Dimer-trimer	35.3°	N
P23	Trimer-trimer	70.5°	N
Helical filaments
Helical‖	Dimer-dimer	Any angle,	N

This table gives only those symmetries that can be constructed by combining two oligomerization domains of the dimeric or trimeric type. Other kinds of oligomerization domains, such as tetramers, would give additional possibilities not listed here. 

^*T, O, I, and D_n refer to tetrahedral, octahedral, icosahedral, and dihedral symmetry, respectively. The remaining symbols are denoted by their Hermann–Mauguin symbols. 

^† The angle formed between the two symmetry elements is given, followed by I or N to denote intersecting or nonintersecting axes. 

^‡ See Fig. 2c. 

^§ See Fig. 1e. 

^¶ See Fig. 1d. 

^‖ See Fig. 3b.