What Is a Polyhedron?

A polyhedron is a solid surrounded by four or more polygons. It has three related definitions. In the traditional sense, it is a three-dimensional polymorph, and in the updated sense, it is a bounded or unbounded generalization of a polymorph in any dimension. By further generalizing the latter, a topological polyhedron is obtained.

In the classic sense, a polyhedron (English word from the Greek , poly- is the root , which means "multi", + -edron, from , which means "base", "pedestal", or "face" ) Is a three-dimensional shape. It consists of a finite number of polygonal faces. Each face is a part of a plane. The faces intersect at edges. Each edge is a straight line segment, and the edges intersect at a point, called a vertex.

A regular polyhedron, or Platonic solid, refers to a convex polyhedron whose faces are all congruent regular polygons and the number of faces connected to each vertex is the same. So for every two vertices there is an equidistant

Polyhedron element

A polyhedron feature is a GIS object that stores a collection of polygons, and can represent the boundaries of a 3D object as a single row in a database. Polygons store texture, color, transparency, and geometric information representing the components of a feature. The geometric information stored in a face can be a triangle, a triangle fan, a triangle strip, or a ring.

All polyhedra store z-values as part of the coordinate system used to construct the faces. Although you can use digital feature attributes to build a base z-value model of a polyhedron, this option may not support the same analysis and interaction options available when using embedded z-values.

Some polyhedron features are considered closed, which means that they correctly define the volume. Closed polyhedra can be used for other analysis tools such as 3D union and 3D intersection. To treat a polyhedron as closed, it must be constructed in the correct way. The features must represent a different volume. The faces that make up the volume must have the same counterclockwise direction as their coordinates and participate in the shell that defines the volume. These faces must not intersect each other, and there must be no gaps or empty spaces in the shell. You can use the Close Geoprocessing tool to verify that the polyhedron is closed properly.

Examples of polyhedron features include textured buildings, light poles, trees, subsurface strata, underground buildings, or some type of analysis surface.

Create a polyhedron feature class

To create a new polyhedron feature class, simply select Polyhedron Feature from the Type drop-down menu when defining the geometry of the feature class.

z-value

Z values are used to represent the shape and elevation of polyhedron features. It can represent absolute height or height relative to the ground. Both methods are fully supported when displaying and analyzing the generated 3D feature classes.

The unit and datum of the z-value of the feature class should be defined in the feature dataset where the feature class is located (if one exists) or in the feature class itself (if no feature dataset is available). If the units are not defined, ArcGIS assumes that the units of z match the units of x, y. This assumption can be problematic, especially when the units of x, y are geographic units (latitude-longitude).

Create polyhedron features

Use geoprocessing tools to import existing 3D models into ArcGIS to create polyhedral features. The 3D layer to feature class geoprocessing tool converts points symbolized through various model formats, such as SketchUp, OpenFlight, 3ds, or COLLADA, to a polyhedron feature class. Importing 3D file geoprocessing tools can do the same, but offers more import format options such as VRML. Alternatively, you can use ArcObjects to programmatically construct polyhedron features.