Group Modify Polytope
Creating Group Polytopes produces coordination polyhedra around each central atom, plus a report of topological and geometrical properties.

Throughout the report, Minimum is the minimum value, Maximum is the maximum value, Average is the mean value and Deviation is the standard deviation, in the universe formed by the selected polyhedrons only.

### Polyhedrons

Total number of polyhedrons. Polyhedrons are always External.

### Faces

Total number of faces. Faces are always External.

### Edges

Total number of edges. Edges are always External.

### Vertices

Total number of vertices. Vertices are always External.

### Polyhedron Faces

Number of faces per polyhedron. The minimum value is 4 (tetrahedron).

### Polyhedron Edges

Number of edges per polyhedron. The minimum value is 6 (tetrahedron).

### Polyhedron Vertices

Number of vertices per polyhedron. The minimum value is 4 (tetrahedron).

### Face Vertices

Number of vertices per face. The minimum value is 3 (triangle).

### Vertex Faces

Number of faces sharing a vertex. The minimum value is 3 (system corner).

### Polyhedron Volumes

The volume for each polyhedron, obtained by summing the volumes of all its triangular piramids.

### Polyhedron Areas

The area for each polyhedron, obtained by summing the areas of all its faces.

### Polyhedron Lengths

The length for each polyhedron, obtained by summing the lengths of all its edges.

### Polyhedron Aberrations

This is the Spherical Aberration, the ratio between the area of a polyhedron and the area of a sphere with the same volume. As a sphere is the 3D object with a smaller area/volume ratio, Spherical Aberration is always above 1.0.

### Face Areas

The area for each face, obtained by summing the areas of all its triangles. Faces with an area smaller than a given tolerance (the Area tolerance in the Group->Measure dialog) are removed.

### Face Lengths

The perimeter for each face, obtained by summing the lengths of all its edges.

### Face Aberrations

This is the Circular Aberration, the ratio between the perimeter of a face and the perimeter of a circumpherence with the same area. As a circumpherence is the 2D object with a smaller perimeter/area ratio, Circular Aberration is always above 1.0.

### Edge Lengths

The length for each edge.

### Face Angles

The angle between adjacent faces (between 0 and 180 degrees).
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