Dodecahedron - Two Dimensional Symmetry Projections

Two Dimensional Symmetry Projections

The dodecahedron has two special orthogonal projections, centered, on vertices and pentagonal faces, correspond to the A2 and H2 Coxeter planes.

Orthogonal projections
Centered by Vertex Edge Face
Image
Projective
symmetry
] = ] =

In perspective projection, viewed above a pentagonal face, the dodecahedron can be seen as a linear-edged schlegel diagram, or stereographic projection as a spherical polyhedron. These projections are also used in showing the four dimensional 120-cell, a regular 4-dimensional polytope, constructed from 120 dodecahedra, projecting it down to 3-dimensions.

Perspective projections
Polyhedron Spherical

Read more about this topic:  Dodecahedron

Famous quotes containing the words dimensional, symmetry and/or projections:

    I don’t see black people as victims even though we are exploited. Victims are flat, one- dimensional characters, someone rolled over by a steamroller so you have a cardboard person. We are far more resilient and more rounded than that. I will go on showing there’s more to us than our being victimized. Victims are dead.
    Kristin Hunter (b. 1931)

    What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.
    George Gordon Noel Byron (1788–1824)

    Western man represents himself, on the political or psychological stage, in a spectacular world-theater. Our personality is innately cinematic, light-charged projections flickering on the screen of Western consciousness.
    Camille Paglia (b. 1947)