s101021206陳益昇幾何作圖

幾何作圖

作者:數學16陳益昇
學號:101021206

I.polyhedron compoud in polyhedron


5 crossed cubes compound in a dodecahedron	5 crossed tetrahedrons compound in a dodecahedron(inside to outside)	5 crossed tetrahedrons compound in a dodecahedron(onside to inside)	5 octahedra compound in a dodecahedron

Dodecahedron & tetrahedron	Golden rectangle	rhombic icosahedron in regular octahedron in regular tetrahedron in cube in rhombic dodecahedron	Dodecahedron-Icosahedron Compound

II.the greatest polyhedron inside polyhedron


Greatest Cube inside an regular Dodecahedron	Greatest Icosahedron Inside an Octahedron	Greatest Icosahedron Inside an Tetrahedra	Greatest regular Dodecahedron inside an Cube(method1)

Greatest regular Dodecahedron inside an Cube(method2)	Greatest regular Octahedron inside an Cube(method1)	Greatest regular Octahedron inside an Cube(method2)

III.polyhedron and animation


Animation of Icositetrahedrons	Animation of Rhombic Polyhedron with 132 Rhombic faces	Animation of Rhombohedron	Cube and Octahedron Exchange

Cube distortion	Dual For Cube	Great Rhombicosidodecahedron	jitterbug

Rhombic Dodecahedron By Half-sphere	Rhombic triacontahedron inscribed in a cube	Great Rhombicosidodecahedron	Rhombicuboctahedron

Rhombohedrons in Dodecahedron	square cupola	triangular cupola	Truncated cuboctahedron

Variations of Deltoidal Hexecontahedrons

IV.projection and trajectory


A Ellipse trajectory in 3-Dimensional Space	A Parabola trajectory in 3-Dimensional Space	cube Projected on Rhombic Dodecahedron	Cube Projected on Rhombic triacontahedron

Hexahedron projected on Dodecahedron	Hexahedron projected on Hexahedron	square projection	Tetrahedron Projected on Cube

Tetrahedron Projected on Tetrahedron

V.inversion of polyhedron


20 Inscribed Circles of Faces of Icosahedron Inverted	Cricles Inscribed on Faces of Dodecahedron Inverted	Cricles Inscribed on Faces of Icositetrahedron Inverted	Cricles Inscribed on Faces of Octahedron Inverted

Cricles Inscribed on Faces of Octahedron Inverted

VI.kaleidocycles

VII.Spheres and circles


4 circles tagent to 2 circles on the sphere	4 points concyclic on the sphere	Circle projection to a point on the sphere	four Circles Each Common Tangent to Two Fixed Circles and Their Stereographic Images

Monge's theorem	pappus theorem	poncelet's closure theorem	rotation and revolution

Steiner Porism I	Steiner Porism II	Three-Circle Theorem on Sphere

VIII.surfaces


the torus of 12 villarceau circles	torus	torus-2	villarceau circle