Flatten Icosahedron

Flatten Icosahedron rearranges the faces of an icosahedral virus capsid from Multiscale Models into a plane. This flat view can be saved as an image, printed, and folded into a paper icosahedron model.

Dengue virus 1k4r	flattened (larger version suitable for printing)	folded paper model

There are several ways to start Flatten Icosahedron, a tool in the Higher-Order Structure category.

The capsid subunit coordinates should first be opened in Chimera and the complete capsid generated with Multiscale Models using Icosahedral symmetry, xyz 2-fold axes (VIPER). This is done automatically when a structure is fetched from the Virus Particle Explorer database (VIPERdb) or a local VIPER file is read. This tool will not work on structures that are not multiscale models, even if they have the correct type of symmetry. All multiscale models present will be affected.

When Flatten is clicked, the twenty triangular faces of an icosahedral capsid are laid out in a plane. The orientations of the faces relative to the structure are assumed based on the known symmetry. Each chain is associated with the triangular face whose center is closest to the geometric center of the chain. To generate the planar arrangement, a common rotation and translation are applied to all the chains of a given face. The chains and faces remain three-dimensional; each face is simply repositioned relative to the others. Unflatten reverses the process. Close dismisses the Flatten Icosahedron dialog, and Help opens this manual page in a browser window.

• The Radius controls the spacing of faces in the plane. If an ideal tetrahedron were flattened using a radius equal to that of the smallest sphere it fits within, the triangular faces would exactly abut. Larger radii would generate triangles in the flattened state larger than the faces of the original ideal tetrahedron. If the Radius field is blank, the largest distance between the capsid center and an atom in the capsid will be used. Changes in the value can be applied by clicking Flatten (it is not necessary to unflatten before reflattening).
• Show triangle mesh indicates whether the triangles should be outlined in the flattened state. The lines can be used as guides for cutting and folding to produce a paper model. The color of the lines can be specified by clicking the color well and using the Color Editor. The lines can be moved in front of the plane (so that they are not obscured by parts of the structure) by entering a z offset value and pressing Enter (return).
• Use orthographic camera mode turns off perspective. This is important for generating an undistorted image of the flattened tetrahedron. The projection mode (perspective or orthographic) can also be controlled with the Camera tool. Further, it is important to keep the plane of the flattened structure normal to the line of sight. If the structure was rotated after flattening, the correct orientation can be restored with the command reset.

1m1c flattened	1m1c flattened and tiled

Tiling. Cutting and folding to make a paper model chops away parts of proteins that straddle triangle boundaries. Tiling the image allows parts of a cut protein to appear on both sides of the cut lines when taped together. Tiling is not necessary, but improves the appearance of the final model. Currently, Chimera cannot perform the tiling, so a separate image-editing program must be used. GIMP was used in the example shown here. Steps:

• Create a flat icosahedron image in Chimera with a transparent background. If system hardware permits, background transparency can be enabled in the Effects tool. (Only high-end graphics cards support this feature; if not available, use the image-editing program to make the background transparent instead.)
• In the image-processing program, make four copies of the image and place them around the border of the original image. In GIMP, this is done using "duplicate layer" and the "move layer" mouse mode. The "stacking order" of the image copies may affect the appearance. In this example, the four surrounding copies were placed below the original image. The resulting tiling is not perfect; ideally, along a border the copy should be above the original in some places and below it in others.

Known icosahedral symmetry. This tool uses the icosahedral reference frame where 2-fold axes are along the x, y and z axes, called Icosahedral symmetry, xyz 2-fold axes (VIPER) in the Multiscale Models dialog. To use a different reference frame requires a small change to the Python code. Specifically, you would change the '222' in file share/FlattenIcosahedron/__init__.py to '222r', or '2n5', or '2n3'. Refer to file share/Icosahedron/__init__.py for the definitions of these alternate reference frames.