The Augmented Pentagonal Prism
The augmented pentagonal prism (J52) is the 52nd Johnson solid. It has 11 vertices, 19 edges, and 10 polygons (4 triangles, 4 squares, and 2 pentagons).
It can be constructed augmenting a pentagonal prism with a square pyramid. A second square pyramid can be added in one of the non-adjacent positions of the prism to make a biaugmented pentagonal prism (J53).
Projections
Here are some views of the augmented pentagonal prism from various angles:
| Projection | Description |
|---|---|
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Top view. |
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Front view. |
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Side view. |
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72° rotated side view. |
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144° rotated side view. |
Coordinates
The Cartesian coordinates of the augmented pentagonal prism, centered on the origin and with edge length 2, are:
- (0, √((10+2√5)/5), ±1)
- (±φ, √((5−√5)/10), ±1)
- (±1, −√((5+2√5)/5), ±1)
- (0, −(√2 + √((5+2√5)/5)), 0)
where φ=(1+√5)/2 is the Golden Ratio.
