# Omniaugmented dodecahedral prism (EntityTopic, 13)

### From Hi.gher. Space

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The '''omniaugmented dodecahedral prism''' is a [[CRF polytope]] with 2 [[dodecahedra]], 24 [[pentagonal pyramid]]s, and 60 [[square pyramid]]s. It is constructed by augmenting the pentagonal prisms of the [[dodecahedral prism]] with [[pentagonal prism pyramid]]s. Its lace tower is (x5o3o || o5o3A || x5o3o) or xox5ooo3oAo, where A = {{Over|3|√5}}. | The '''omniaugmented dodecahedral prism''' is a [[CRF polytope]] with 2 [[dodecahedra]], 24 [[pentagonal pyramid]]s, and 60 [[square pyramid]]s. It is constructed by augmenting the pentagonal prisms of the [[dodecahedral prism]] with [[pentagonal prism pyramid]]s. Its lace tower is (x5o3o || o5o3A || x5o3o) or xox5ooo3oAo, where A = {{Over|3|√5}}. |

## Latest revision as of 20:58, 19 September 2018

The **omniaugmented dodecahedral prism** is a CRF polytope with 2 dodecahedra, 24 pentagonal pyramids, and 60 square pyramids. It is constructed by augmenting the pentagonal prisms of the dodecahedral prism with pentagonal prism pyramids. Its lace tower is (x5o3o || o5o3A || x5o3o) or xox5ooo3oAo, where A = ^{3}∕_{√5}.

## Projections

Centered on dodecahedron:

Side view:

Close-up projective view without visibility clipping, showing all 3 layers concentrically:

## Coordinates

# x5o3o: apacs<phi, phi, phi> ~ <±1> epacs<0, 1, phi^2> ~ <±1> # o5o3A: (3/√5)*epacs<1, 0, phi> ~ <0>