# 3.3.3.56. NXcg_tetrahedron_set¶

**Status**:

base class, extends NXobject

**Description**:

## Computational geometry description of a set of tetrahedra in Euclidean space. ...

Computational geometry description of a set of tetrahedra in Euclidean space.

The tetrahedra do not have to be connected. As tetrahedral elements they are among hexahedral elements one of the most frequently used geometric primitive for meshing and describing volumetric and surface descriptions of objects at the continuum scale.

A set of tetrahedra in 3D Euclidean space.

The tetrahedra do not have to be connected, can have different size, can intersect, and be rotated.

Tetrahedra are the simplest and thus important geometrical primitive. They are frequently used as elements in finite element meshing/modeling.

Tetrahedra have to be non-degenerated, closed, and built of triangles which are not self-intersecting.

**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 tetrahedra.

**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 tetrahedra.

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

face_area: (optional) NX_NUMBER (Rank: 2, Dimensions: [c, 4]) {units=NX_AREA}Area of each of the four triangular faces of each tetrahedron.

edge_length: (optional) NX_NUMBER (Rank: 2, Dimensions: [c, 6]) {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 tetrahedra. 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 tetrahedra 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

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

A simple approach to describe the entire set of tetrahedra when the main intention is to store the shape of the tetrahedra for visualization. should take the possibility to describe

tetrahedron: (optional) NXcg_face_list_data_structureDisentangled representations of the mesh of specific tetrahedra.

tetrahedron_half_edge: (optional) NXcg_half_edge_data_structure## Disentangled representation of the planar graph that each tetrahedron ...

Disentangled representation of the planar graph that each tetrahedron 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.