public static void AddZAxis(Model3DGroup group,
                                    double length = 4, double thickness = 0.1)
        {
            MeshGeometry3D mesh   = new MeshGeometry3D();
            Point3D        origin = D3.Origin -
                                    D3.XVector(thickness / 2) -
                                    D3.YVector(thickness / 2) -
                                    D3.ZVector(thickness / 2);

            mesh.AddBox(origin,
                        D3.XVector(thickness), D3.YVector(thickness), D3.ZVector(length));
            group.Children.Add(mesh.MakeModel(Brushes.Blue));
        }
        // Make a cube at the origin.
        public static void AddOrigin(Model3DGroup group,
                                     double cubeThickness = 0.102)
        {
            MeshGeometry3D mesh   = new MeshGeometry3D();
            Point3D        origin = D3.Origin -
                                    D3.XVector(cubeThickness / 2) -
                                    D3.YVector(cubeThickness / 2) -
                                    D3.ZVector(cubeThickness / 2);

            mesh.AddBox(origin,
                        D3.XVector(cubeThickness),
                        D3.YVector(cubeThickness),
                        D3.ZVector(cubeThickness));
            group.Children.Add(mesh.MakeModel(Brushes.Black));
        }
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        // Define the model.
        private void DefineModel(Model3DGroup group)
        {
            //// Verify the dodecahedron calculations.
            //MeshExtensions.VerifyDodecahedron();

            // Show the axes.
            MeshExtensions.AddAxes(group);

            const double scale = 1.25;

            // Make a solid insphere.
            MeshGeometry3D mesh1 = new MeshGeometry3D();

            mesh1.AddSphere(D3.Origin, G3.DodecahedronInradius(), 60, 30, true);
            mesh1.ApplyTransformation(new ScaleTransform3D(scale, scale, scale));
            group.Children.Add(mesh1.MakeModel(Brushes.Red));

            // Make a translucent dodecahedron.
            MeshGeometry3D mesh2 = new MeshGeometry3D();

            mesh2.AddDodecahedron();
            mesh2.ApplyTransformation(new ScaleTransform3D(scale, scale, scale));
            Brush         brush  = new SolidColorBrush(Color.FromArgb(128, 128, 255, 128));
            MaterialGroup group2 = D3.MakeMaterialGroup(
                new DiffuseMaterial(brush),
                new SpecularMaterial(Brushes.White, 100));

            group.Children.Add(mesh2.MakeModel(group2));

            // Make a translucent circumsphere.
            MeshGeometry3D mesh3 = new MeshGeometry3D();

            mesh3.AddSphere(D3.Origin, G3.DodecahedronCircumradius(), 60, 30, true);
            mesh3.ApplyTransformation(new ScaleTransform3D(scale, scale, scale));
            MaterialGroup group3 = D3.MakeMaterialGroup(
                new DiffuseMaterial(brush),
                new SpecularMaterial(Brushes.White, 100));

            group.Children.Add(mesh3.MakeModel(group3));
        }