Geometric Construction
Teacher 全任重 老師
Student 康耀文
ID 9861234

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Polyhedron
Dual For Cube Rhombic triacontahedron Cube distortion Variations of Deltoidal Hexecontahedrons Rhombic Dodecahedron By Half-sphere





Rhombohedrons in Dodecahedron
 		Triangular Cupola Square cupola Small Rhombicuboctahedron Great Rhombicuboctahedron





Golden rectangle Samll Rhombicosidodecahedron Great Rhombicosidodecahedron Icositetrahedron Animation of Icositetrahedrons





Inspired by Paper Folding Adjustable Kaleidocycles-5 Adjustable Tight Kaleidocyle Jitterbug






Embedding
Cube & tetrahedron rhombic icosahedron in regular octahedron in regular tetrahedron in cube in rhombic dodecahedron Dodecahedron by Icosahedron Tetrahedron 5-Compound Faces of Icosahedron lie on Faces of Five Tetrahedra





Octahedron 5-Compound Octahedron 5-Compound (Method 2) 5 Cube inside Regular Dodecahedron 5 Cube inside Regular Dodecahedron (Method 2) Greatest Cube Inside an Regular Dodecahedron (Method 1)





Greatest Cube Inside an Regular Dodecahedron (Method 2) Greatest Regular Dodecahedron Inside an Cube (Method 1) Greatest Regular Dodecahedron Inside an Cube (Method 2) Greatest Octahedron Inside an Cube (Method 1) Greatest Octahedron Inside an Cube (Method 2)





Greatest Icosahedron Inside an Tetrahedra (Method 1) Greatest Icosahedron Inside an Tetrahedra (Method 2) Greatest Icosahedron Inside an Octahedron







Projection
Cube Projected on Cube(Method1) Cube Projected on Cube(Method2) Cube Projected on Regular Dodecahedron Tetrahedron Projected on Tetrahedron Tetrahedron Projected on Cube





Circle projection to a point on the sphere Three-Circle Theorem on Sphere Three Triangulars of two circles and their inverse relative to the sphere Cube Projected on Rhombic Dodecahedron Cube Projected on Rhombic triacontahedron





Trajectory
A Parabola in 3-Dimensional Space Conic Section A Parabola trajectory in 3-Dimensional Space Two Perspetive Quadrilaterals Having One Point in Common Circle Trajectory in lateral direction





Circle Trajectory in vertical direction Villarceau circles Villarceau circles-12 Triangle Torus and Tangent Trajectory of intersection curve of sphere and the plane which is perpendicular to diameter





Trajectory of intersection curve of sphere and the plane outside the sphere Trajectory of intersection curve of sphere and the plane which orthogonal to the sphere with a line








Inversion
Inversion practice I Inversion practice II Inversion circle will be the projection to the center of orthogonal sphere Inversion wrt big sphere of a circle is the projection on the small sphere,which means small sphere is  the inversion of plane The relation of the circles on the plane is same as the relation of  inversion circles on small sphere which is the inversion of the plane





Four Circles Each Common Tangent to Two Fixed Circles and Their Stereographic Images Circles and there Inversion  Relationship  Inversion of Circles of 6 different connect points in two intersecting line Asymmetric Steiner Porism Inversion of Circles Inscribed in the Faces of Regular Icosahedron





Inversion of Circles Inscribed in the Faces of Regular Octahedron Inversion of Inscribed Circles of Faces of Square Cupola Inversion of Inscribed Circles of Faces of Great Rhombicuboctahedron Two circles on sphere inversed by the orthogonal sphere with same axis Asymmetric Design Based on Regular Octahedron





Asymmetric Design Based on Triangular Cupola









Else
Animation of Rhombic Polyhedron with 132 Rhombic faces Desargues' Theorem in 3D Common Tangent Cones of Three Spheres Steiner Porism I Steiner Porism II