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This node generates spherical objects of different geometry types. It is capable of creating nonuniform scalable spheres of all geometry types.
If an input is provided, the sphere’s radius is automatically determined as a function of the input’s bounding geometry.
This Operation is used to create spheres and ellipsoids. Clicking and dragging the mouse on the Construction Plane generates a sphere whose radii are specified by your drag.
Placing a Sphere in the viewer
To...  Do this 

Place a sphere anywhere in the scene 

Place a sphere at the origin 
Sphere Handles
There are special handles available at the geometry level for the sphere object that allow you to stretch and squash it.

Move to the geometry level by double clicking LMB the sphere node in the network editor or by clicking the Jump to Operator button on the operation controls toolbar.

Drag the handles to squash or stretch the sphere.
Parameters
Primitive Type
Type of geometry to create.
Connectivity
Rows
Creates horizontal lines, which are open polygons.
Column
Creates vertical lines, which are open polygons.
Rows & Cols
Both Rows and Columns. All polygons are open.
Triangles
Builds the grid with triangles.
Quads
Creates foursided quadrilaterals.
Alternating Triangles
Creates the grid using alternating triangles.
Radius
This is the X radius of an ellipsoid that is placed if you click on the Construction Plane without dragging. If you click and drag, the size of the sphere is overridden by the amount of drag. Entering nonequal values in the xyz fields results in ellipsoidal shapes.
The X radius is defined by the distance dragged from the center, while the Y and Z radii vary proportionally with the X / Y and X / Z ratios in the parameter dialog.
Center
Determines the location of the center of the ellipsoid. This value is updated whenever you click (and drag) to create an ellipsoid. A new ellipsoid center will be positioned here if you hit Enter.
Rotation
Rotation about the center of the ellipsoid.
Uniform Scale
Uniform scaling.
Orientation
Poles of sphere align with orientation axis.
Frequency
Increases or decreases the number of polygons which make up a polygonal sphere. The higher the frequency, the smoother the sphere. It is disabled if building a sphere of a type other than polygonal.
Rows
The number of rows of a mesh or imperfect NURBS / Bezier sphere. The more rows and columns, the rounder the sphere. A NURBS or Bezier sphere should have at least order1 rows and columns. Rows are associated with the V directions and columns with the U parametric direction.
Columns
Number of columns in the sphere.
U Order
Sets the U spline order of the NURBS or Bezier surface when building a sphere of one of these two types. The lowest order is 2 (linear); the highest is 11. Cubic spheres are built by default.
V Order
Order of NURBS/Bezier curve in V direction.
U Wrap
Wraps the surface in the U direction.
Imperfect
Specifies whether the NURBS / Bezier sphere should be built using rational or nonrational splines. A perfect sphere has a rational topology, one that associates nonunit weights with certain vertices. Furthermore, a perfect sphere has a predefined number and positions of CVs for any given spline order. An imperfect sphere is nonrational and its number of CVs isn’t that strictly determined by its order.
Rational spheres built this way yield a mathematically perfect shape; however, given their special definition, perfect spheres are not always the ideal choice for further modeling of their points. Besides, they represent heavier geometry and may put more pressure both on the cpu and ram. In practice, you will find imperfect spheres to be a better modeling choice, so it is advisable to build perfect spheres only when perfect shapes are paramount.
Unique Points per Pole
In a meshtype sphere, the meridians meet at the poles of the sphere. This creates a situation where each meridian line contributes its own point to a pole. When this box is not checked, the points are consolidated into a single point shared by all the meridians. Otherwise if checked, the points are all left to be unique.
Accurate Bounds
If the operation is being used to generate a bounding sphere for its input geometry, this parameter tells us to use a more accurate (but slower) bounding sphere calculation.
Triangular Poles
In a polygon mesh sphere, each polygon is logically a quad. However, at the poles, two points become degenerate. If Triangular Poles is enabled, these quads are turned into triangles.
Examples
SphereTypes Example for Sphere geometry node
This example shows all the geometry types the Sphere SOP can create and explains the differences between them.
Choosing the right geometry type can make a network flow and render much faster.