Framework database

This is a module for providing common types of frameworks.

pyrigi.frameworkDB.CnSymmetricFourRegular(n=8)

Return a C_n-symmetric framework.

Todo

use in tests

Definitions

• Example with a free group action

Parameters:

n (int)

Return type:

Framework

pyrigi.frameworkDB.CnSymmetricFourRegularWithFixedVertex(n=8)

Return a C_n-symmetric framework with a fixed vertex. The cyclical group C_n needs to have even order of at least 8.

The returned graph satisfies the expected symmetry-adapted Laman count for rotation but is infinitesimally flexible.

Todo

use in tests

Definitions

• Example with joint at origin

Parameters:

n (int)

Return type:

Framework

pyrigi.frameworkDB.Complete(n, d=2)

Return d-dimensional framework of the complete graph on n vertices.

Todo

Describe the generated realization.

Parameters:

• n (int)

• d (int)

Return type:

Framework

pyrigi.frameworkDB.CompleteBipartite(m, n, realization=None)

Return a complete bipartite framework on m+n vertices in the plane.

Parameters:

• realization (str | None) – If "dixonI", a realization with one part on the x-axis and the other on the y-axis is returned. Otherwise (default), a “general” realization is returned.

• m (int)

• n (int)

Return type:

Framework

Todo

Implement realization in higher dimensions.

pyrigi.frameworkDB.Cycle(n, d=2)

Return d-dimensional framework of the n-cycle.

Parameters:

• n (int)

• d (int)

Return type:

Framework

pyrigi.frameworkDB.Diamond()

Framework of the diamond with square realization in the plane

Return type:

Framework

pyrigi.frameworkDB.Frustum(n)

Return the n-Frustum with n vertices in dimension 2.

Definitions

• n-Frustum

Parameters:

n (int)

Return type:

Framework

pyrigi.frameworkDB.K33plusEdge()

Return a framework of the complete bipartite graph on 3+3 vertices plus an edge.

Return type:

Framework

pyrigi.frameworkDB.Path(n, d=2)

Return d-dimensional framework of the path graph on n vertices.

Parameters:

• n (int)

• d (int)

Return type:

Framework

pyrigi.frameworkDB.Square()

Framework of the 4-cycle with square realization in the plane

Return type:

Framework

pyrigi.frameworkDB.ThreePrism(realization=None)

Return 3-prism framework.

Parameters:

realization (str | None) – If "parallel", a realization with the three edges that are not in any 3-cycle being parallel is returned. If "flexible", a continuously flexible realization is returned. Otherwise (default), a general realization is returned.

Return type:

Framework

pyrigi.frameworkDB.ThreePrismPlusEdge()

Return a framework of the 3-prism graph with one extra edge.

Return type:

Framework