Symmetry Tetrahedron Animations 8 images tree :: Geometry > Symmetry Tetrahedron Animations
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The Platonic solids can be divided into a number of congruent tetrahedra which share a common vertex at the centre of the solid. The maximum number can be made when the four vertices are the centres of the different dimensional elements of the solid: the centre of the solid itself; a face centre; an edge centre and a vertex (which is its own centre.)

The maximum number of tetrahedra is also the number of symmetries of the solid, and any symmetry of the solid maps the set of tetrahedra onto itself. The tetrahedra have no mirror symmetry.

The following animations rearrange the symmetry unit tetrahedra, sometimes grouped together, in various ways. The tetrahedra are coloured black and white according to their handedness. The animations preserve the rotational symmetry of the base polyhedron.

 Image List

Tetrahedron  Med    Lrg
 Description : White tetrahedra are rotated about axes through the edge centres. Black tetrahedra are rotated about axes through the face centres. view animation (1.0Mb)

Tetrahedron  Med    Lrg
 Description : A tetrahedron is rearranged into its dual (in a round about way.) view animation (1.4Mb)

Tetrahedron  Med    Lrg
 Description : A tetrahedron is rearranged into its dual. The rotation axes are half way along the line joining a face centre to a vertex. view animation (1.9Mb)

Cube  Med    Lrg
 Description : A cube is rearranged into a stellation of the rhombic dodecahedron. The tetrahedra overlap. view animation (1.9Mb)

Cube  Med    Lrg
 Description : A cube is rearranged into a rhombic dodecahedron. The rhombic dodecahedron has a hollow centre the same shape and size as the original cube. view animation (2.4Mb)

Cube  Med    Lrg
 Description : The cube faces are the bases of pyramids with an apex at the cube centre. The pyramids travel through the cube until their bases meet and and they form a stellation of the rhombic dodecahedron which has half the volume of the cube. Finally the pyramids lie on the outside of the cube forming a rhombic dodecahedron with twice the volume of the cube (discounting the hollow cube inside of it.) view animation (2.9Mb)

Dodecahedron  Med    Lrg
 Description : The dodecahedron faces are the bases of pyramids with an apex at the dodecahedron centre. The pyramids travel through the dodecahedron until their bases coincide with the opposite faces, pausing briefly at the halfway stage where the bases meet. view animation (3.0Mb) Here are some of the interesting stages as VRML models, having convex hulls of an icosidodecahedron. This is quite similar to a dodecadodecahedron truncated dodecahedron, rhombic triacontahedron, icosahedron. althought the 'inner' vertices don't lie on the hull

Dodecahedron  Med    Lrg
 Description : The dodecahedron faces are the bases of pyramids with an apex at the dodecahedron centre. The pyramids travel through the dodecahedron until their bases coincide with the opposite faces, pausing briefly at the halfway stage where the bases meet. The pyramids rotate through a half-turn about their axis as they travel to the other side. view animation (2.4Mb) Here are some of the interesting stages as VRML models. Stage A Stage B (the convex hull is not quite a snub dodecahedron) Stage C (the mid-point, an intersection of five pentagonal dipyramids) Stage D Stage E Stage F (the pyramids lie on the outside of a dodecahedron) Stage G (not in order) Stage H (not in order)