# 3.3.3.52. NXcg_polyhedron_set¶

**Status**:

base class, extends NXobject

**Description**:

## Computational geometry description of a polyhedra in Euclidean space. ...

Computational geometry description of a polyhedra in Euclidean space.

Polyhedra, also so-called cells (especially in the convex of tessellations), here described have to be all non-degenerated, closed, built of and thus built out of not-self-intersecting polygon meshes. Polyhedra may make contact, so that this base class can be used for a future description of tessellations.

For more complicated manifolds and especially for polyhedra with holes, users are advised to check if their particular needs are described by creating (eventually customized) instances of an NXcg_polygon_set, which can be extended for the description of piecewise-linear complexes.

**Symbols**:

The symbols used in the schema to specify e.g. dimensions of arrays.

c: The cardinality of the set, i.e. the number of polyhedra.

n_e_total: The total number of edges for all polyhedra.

n_f_total: The total number of faces for all polyhedra.

**Groups cited**:NXcg_face_list_data_structure, NXcg_half_edge_data_structure, NXcg_unit_normal_set, NXtransformations

**Structure**:

dimensionality: (optional) NX_POSINT {units=NX_UNITLESS}Obligatory value:

`3`

cardinality: (optional) NX_POSINT {units=NX_UNITLESS}

volume: (optional) NX_NUMBER (Rank: 1, Dimensions: [c]) {units=NX_VOLUME}Interior volume

center: (optional) NX_NUMBER (Rank: 2, Dimensions: [c, 3]) {units=NX_LENGTH}## Position of the geometric center, which often is but not necessarily ...

Position of the geometric center, which often is but not necessarily has to be the center_of_mass of the polyhedra.

surface_area: (optional) NX_NUMBER (Rank: 1, Dimensions: [c]) {units=NX_AREA}Total surface area as the sum of all faces.

number_of_faces: (optional) NX_POSINT (Rank: 1, Dimensions: [c]) {units=NX_UNITLESS}## The number of faces for each polyhedron. Faces of adjoining polyhedra ...

The number of faces for each polyhedron. Faces of adjoining polyhedra are counted for each polyhedron. This field can be used to interpret the array/field with the individual area values for each face.

face_area: (optional) NX_NUMBER (Rank: 1, Dimensions: [n_f_total]) {units=NX_AREA}Area of each of the four triangular faces of each tetrahedron.

number_of_edges: (optional) NX_POSINT## The number of edges for each polyhedron. Edges of adjoining polyhedra ...

The number of edges for each polyhedron. Edges of adjoining polyhedra are counterd for each polyhedron. This field can be used to interpret the array/field with the individual length for each edge.

edge_length: (optional) NX_NUMBER (Rank: 1, Dimensions: [n_e_total]) {units=NX_LENGTH}Length of each edge of each tetrahedron.

identifier_offset: (optional) NX_INT {units=NX_UNITLESS}## Integer which specifies the first index to be used for distinguishing ...

Integer which specifies the first index to be used for distinguishing polyhedra. Identifiers are defined either implicitly or explicitly. For implicit indexing the identifiers are defined on the interval [identifier_offset, identifier_offset+c-1]. For explicit indexing the identifier array has to be defined.

The identifier_offset field can for example be used to communicate if the identifiers are expected to start from 1 (referred to as Fortran-/Matlab-) or from 0 (referred to as C-, Python-style index notation) respectively.

identifier: (optional) NX_INT (Rank: 1, Dimensions: [c]) {units=NX_UNITLESS}Integer used to distinguish polyhedra for explicit indexing.

TRANSFORMATIONS: (optional) NXtransformations## Reference to or definition of a coordinate system with ...

Reference to or definition of a coordinate system with which the qualifiers and mesh data are interpretable.

vertex_normal: (optional) NXcg_unit_normal_set

edge_normal: (optional) NXcg_unit_normal_set

face_normal: (optional) NXcg_unit_normal_set

polyhedra: (optional) NXcg_face_list_data_structure## A simple approach to describe the entire set of polyhedra when the ...

A simple approach to describe the entire set of polyhedra when the main intention is to store the shape of the polyhedra for visualization.

polyhedron: (optional) NXcg_face_list_data_structureDisentangled representations of the mesh of specific polyhedron.

polyhedron_half_edge: (optional) NXcg_half_edge_data_structure## Disentangled representation of the planar graph that each polyhedron ...

Disentangled representation of the planar graph that each polyhedron represents. Such a description simplifies topological processing or analyses of mesh primitive operations and neighborhood queries.

## Hypertext Anchors¶

List of hypertext anchors for all groups, fields, attributes, and links defined in this class.