# Omniaugmented dodecahedral prism (EntityTopic, 13)

(Difference between revisions)
 Revision as of 19:36, 19 September 2017 (view source) (Add approximate FLD)← Older edit Latest revision as of 19:37, 19 September 2017 (view source) (Just leaving that in the history) Line 3: Line 3: | dim=4 | dim=4 | extra={{STS Polytope | extra={{STS Polytope - | flayout={{FLD2|dim=4|left=e3|erev2|a5|line|a5|line2|atbend2|line|atvertbvert2|tline2|atvertbvert2|end|e5}} - {{FLD2|dim=4|left=gap|gap|gap|gap|gap|gap|gap|gap|gap|gap|gap|erev|a2tvert|linetleft}} }}}} }}}} 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 19:37, 19 September 2017

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>
```