Available versions of this document: latest release, release 4.0, release 3.6, release 3.5, nightly master
Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
BigObject PlanarNet<Scalar>
from application fan
A special big object class devoted to planar unfoldings of 3polytopes. Its main functionality is the visualization.
 Type Parameters:
Scalar
: numeric data type used for the coordinates, must be an ordered field. Default isRational
. derived from:
 Example:
To visualize a planar net of some Johnson solid (with flaps, such that you can print, cut and glue):
> planar_net(polytope::johnson_solid(52))>VISUAL>FLAPS;
Properties
Combinatorics
These properties capture combinatorial information of the object. Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.

DUAL_TREE
The spanning tree in the
DUAL_GRAPH
which defines the layout. Endoded as a list of edges, directed away from the root facet. Indices correspond toMAXIMAL_POLYTOPES
as well asFACETS
. Type:

FLAPS
List of directed edges in the primal graph
GRAPH
which need flaps for gluing. Indices correspond toVERTICES
. The orientation is chosen such that the facet in the layout is always on the left. In fact, the flaps define a spanning tree ofGRAPH
. Type:

VF_MAP
Map which tells which vertex/facet pair of the 3polytope is mapped to which vertex of the planar net. The dependence on the facets comes from the fact that most
VERTICES
occur more than once in the planar net. The inverse isVF_MAP_INV
. Type:

VF_MAP_INV
Map which tells how the
VERTICES
of the planar net are mapped to theVERTICES
of the 3polytope. Inverse ofVF_MAP
. Type:

VIF_CYCLIC_NORMAL
Counter clockwise ordering of the
VERTICES
in eachMAXIMAL_POLYTOPES
. This is a copy of the propertyVIF_CYCLIC_NORMAL
ofPOLYTOPE
. Type:
Geometry
These properties capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.

POLYTOPE
The corresponding 3polytope.
 Type:
Polytope<Scalar>
Methods
Visualization
These methods are for visualization.

VISUAL()
This function is the main purpose of the entire class
PlanarNet
. Options:
 option list
Visual::Polygons::decorations
 Returns: