Tuesday, March 2
Space: How do we understand objects in space? Continued..
Symmetries (Isometries) in the plane compared to those in space- an introduction:
Spatial Symmetry
The Platonic and Archimedean Solids
.
Cubeoctahedron
Rhombicubeoctahedron
Icosidodecahedron
Translations
Rotations: Center point - central axis
Reflection : across line - across plane
Symmetries of the octhaedron:
Rotations
reflections
rotation- reflection
Activity. Symmetries of the Cube.
Isometries in space: products of reflections in space:
Rotations and translations
Applications to dance
Polyhedra and Duality
In space: Dual polyhedron.
Connected by counting and constructions.
Vertex - Face
edge-edge
Cube- octahedron;
Dodecahedron - icosahedron; tetrahedron.
Platonic (regular convex polyhedra) and Archimedean (semiregular convex) Solids-
on the web
!
The 5 Platonic Solids
Cube
Dodecahedron
Icosahedron
Octahedron
Tetrahedron
The Archimedean Solids in more detail [Handout!]
The 13 Archimedean Solids
Cubeoctahedron
Icosidodecahedron
Rhombicubeoctahedron
Rhombicosidodecahedron
Rhombitruncated Cubeoctahedron
Rhombitruncated Icosidodecahedron
Snub Cube
Snub Dodecahedron
Truncated Cube
Truncated Dodecahedron
Truncated Icosahedron
Truncated Octahedron
Truncated Tetrahedron
More on The regular and semiregular polyhedra: Check this site! from
Visual geometry pages
.
The Pseudo-Rhombicubeoctahedron.
Getting familiar with the cube and octahedron with shadows.