See: Description
Class  Description 

AxisLinesRGB 
AxisLinesRGB shows 3 redgreenblue (RBB) perpendicular lines suitable as XYZ axes.

CapsuleComparison 
CapsuleComparison shows three capsules, using polygons/lines/points rendering, each a hollow cylinder with hemispherical end caps.

CapsuleGenerator 
Capsule has top and bottom hemispheres with connected sides, with adjustable parameters in the contained Script fields.

Catenary 
A catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.

CubeWithLabeledSides 
Cubeshaped test model with faces on each side individually labeled.

CylinderIndexedFaceSet 
Construct a Cylinder using IndexedFaceSet.

Dodecahedron 
Dodecahedron is a 12sided polyhedron with 30 edges, 20 vertices and 12 pentagonal faces.

ExtrusionEdgeCases 
Scene incorporating extrusion edge cases.

ExtrusionExamplesTest 
Extrusion examples for testing and debugging.

Hemisphere 
Hemisphere is a half sphere.

Icosahedron 
Icosahedron is a polyhedron with 12 vertices and, 20 faces, where a regular icosahedron is a Platonic solid.

IcosahedronSubdivisionLevel1 
Icosahedron is a polyhedron with twenty faces, subdivided to level 1, where all 42 vertices and 80 faces produce regular (equilateral) triangles.

IcosahedronSubdivisionLevel2 
Icosahedron is a polyhedron with twenty faces, subdivided to level 2, where all 162 vertices and 320 faces produce regular (equilateral) triangles.

IcosahedronSubdivisionLevel3 
Icosahedron is a polyhedron with twenty faces, subdivided to level 3, where all 642 vertices and 1280 faces produce regular (equilateral) triangles.

IcosahedronSubdivisionLevel4 
Icosahedron is a polyhedron with twenty faces, subdivided to level 4, where all 2562 vertices and 3366 faces produce regular (equilateral) triangles.

IcosahedronSubdivisionLevel5 
Icosahedron is a polyhedron with twenty faces, subdivided to level 5, where all 10242 vertices and 20480 faces produce regular (equilateral) triangles.

MobiusExtrusion 
Mobius (or Mobius) is a surface with only one side and only one boundary component.

Octahedron 
Octahedron is an 8sided polyhedron with 6 vertices, 8 triangular faces and 12 edges.

ParallelepipedExamples 
Example use of external prototype declaration for Parallelepiped, which is a 3D figure formed by six parallelograms.

ParallelepipedPrototype 
Reusable prototype for creating a Parallelepiped, which is a 3D figure formed by six parallelograms; also sometimes referred to as a rhomboid.

RoundedRectangle2D 
RoundedRectangle2D shows and IndexedFaceSet shape for a flat RoundedRectangle.

RoundedRectangleComparison 
RoundedRectangleComparison shows three RoundedRectangle shapes using polygons/lines/points rendering.

RoundedRectanglePrimitives 
Illustrates how to build rounded rectangle using only primitive nodes.

SphereWithThreeCircumferenceRings 
Semitransparent Sphere with circumference circles on xyz planes to facilitate user rotation of an object, suitable for use as rotation widget.

StairStepPrototype 
Build one or more stair steps, in a straight line.

Teapot 
A watertight (solid) Utah Teapot Model converted from obj format.

Teapots 
Four watertight (solid) Utah Teapot Models converted from obj format.

Tetrahedron 
Tetrahedron is an 8sided pyramidal polyhedron with 4 vertices, 4 triangular faces and 6 edges.

TriangleBlackLines 
Simple Triangle with black lines, illustrating default line rendering.

TriangleWithNumbers 
Simple Triangle with labeled points, where labels always face the user and stay in place with the triangle.

This chapter illustrates design patterns and best practices for authoring different geometries through a collection of interesting 3D shapes.
The opensource
Meshlab
and
X3DEdit
authoring tools helped create many of these examples.
Tools of interest for generating mathematical shapes include:

Copyright ©20052019 Web3D Consortium under an opensource license, free for any use. Feedback is welcome.