The **hkcage** command creates a cage of hexagons and pentagons to
represent the arrangement of proteins in an icosahedral virus capsid.
See also:
**marker**,
**Cage Builder**

The arrangement of subunits in an icosahedral capsid can be described
as a sheet of hexagons in which curvature is introduced by replacing
certain hexagons with pentagons, as in a geodesic dome.
The pentagons occupy the points of the icosahedron, while
the indices *h* and *k* refer to the number and arrangement
of hexagons in each face. A virus T number
(T = *h*^{2} + *hk* + *k*^{2})
is proportional to the number of subunits in the capsid.
VIPERdb
includes viruses with T = 1, 3, 4, 7, 13, and in a few cases, even higher.
For more details, see the
VIPERdb description and the following reference:

Quasi-equivalent viruses: a paradigm for protein assemblies. Johnson JE, Speir JA.The argumentsJ Mol Biol.1997 Jun 27;269(5):665-75.

The basic T number equation describes lattices built from repeats
of the same asymmetric unit. However, expanded versions of the lattices
are possible for capsids with vertices occupied by different proteins
or different domains. For a given T number,
the number of hexagons and pentagons remains the same,
but the total surface area increases by a factor α
due to additional polygons (triangles and squares). Such expanded lattices
can be constructed with the **alpha** option.

The cage is centered at (0,0,0).
It is created as a marker model
unless **mesh true**
is used to specify a surface model instead.
Hexagons are bent where they cross from one triangular face
of the icosahedron to another, so that certain “hexagon” edges
are formed by two straight segments rather than one.

radiuscage-radius

Set cage size, wherecage-radiusis the distance from the center of the icosahedron to a 5-fold vertex (default100.0in physical distance units).

edgeRadiusstick-radius

Set marker modelstick-radius(default 1% of thecage-radius). See also:size

orientationtype

Thetypeof icosahedral orientation can be:

222(default) – with two-fold symmetry axes along the X, Y, and Z axes- 2n5 – with two-fold symmetry along X and 5-fold along Z
- n25 – with two-fold symmetry along Y and 5-fold along Z
- 2n3 – with two-fold symmetry along X and 3-fold along Z
- 222r – same as 222 except rotated 90° about Z
- 2n5r – same as 2n5 except rotated 180° about Y
- n25r – same as n25 except rotated 180° about X
- 2n3r – same as 2n3 except rotated 180° about Y

sphereFactorf

Specify the the weight of the sphere component in an interpolation between an icosahedron and a sphere of equal radius. The sphere factorfranges from0.0(default, icosahedron) to 1.0 (sphere). The interpolation only involves vertex positions and will not generate curved mesh lines.

alphaalphatype

Capsids in which the vertices are occupied by different proteins or domains (rather than identical asymmetric units) may form expanded versions of the lattices, as described in:The missing tailed phages: Prediction of small capsid candidates. Luque A, Benler S, Lee DY, Brown C, White S.Microorganisms.2020 Dec 8;8(12):1944.

Structural puzzles in virology solved with an overarching icosahedral design principle. Twarock R, Luque A.Nat Commun.2019 Sep 27;10(1):4414.The

alphaoption allows creating such expanded lattices, with choices foralphatype(see Fig. 2 in the paper):Thanks to the Luque Lab at San Diego State University for developing the code for this option, with funding from the NSF.

hexagonal(default)- hexagonal-dual
- rhomb
- rhomb-dual
- trihex
- trihex-dual
- snub
- snub-dual

colorcolor-spec

Specify a color for the cage model (defaultwhite).

meshtrue |false

Whether to create a wire-mesh surface model instead of a marker model. If a surface model is created, a marker model can be generated from it later with the commandmarker fromMesh.

replacetrue| false

Whether to replace an existinghkcagemodel with the new one rather than opening an additional model.

UCSF Resource for Biocomputing, Visualization, and Informatics / November 2021