Pentagonal orthocupolarotunda (EntityTopic, 10)
From Hi.gher. Space
(Difference between revisions)
(stub) |
(coordinates) |
||
Line 5: | Line 5: | ||
}}}} | }}}} | ||
The '''pentagonal orthocupolarotunda''' is the 32nd [[Johnson solid]]. It can be constructed by gluing a [[pentagonal rotunda]] and a [[pentagonal cupola]] at their decagonal faces. | The '''pentagonal orthocupolarotunda''' is the 32nd [[Johnson solid]]. It can be constructed by gluing a [[pentagonal rotunda]] and a [[pentagonal cupola]] at their decagonal faces. | ||
+ | |||
+ | ==Coordinates== | ||
+ | |||
+ | These coordinates give a pentagonal orthocupolarotunda having edge length 2, with its 5-fold axis of symmetry aligned to the Z-axis: | ||
+ | |||
+ | <pre> | ||
+ | # x5o: | ||
+ | <-√((10+2*√5)/5), 0, √((20+8*√5)/5)> | ||
+ | <-√((5-√5)/10), ±φ, √((20+8*√5)/5)> | ||
+ | < √((5+2*√5)/5), ±1, √((20+8*√5)/5)> | ||
+ | |||
+ | # o5f: | ||
+ | < √((20+8*√5)/5), 0, √((10+2*√5)/5)> | ||
+ | <-√((25+11*√5)/10), ±φ, √((10+2*√5)/5)> | ||
+ | < √((5+√5)/10), ±φ^2, √((10+2*√5)/5)> | ||
+ | |||
+ | # x5x: | ||
+ | <±√(3+4*φ), ±1, 0> | ||
+ | <±√(2+φ), ±φ^2, 0> | ||
+ | <0, ±2*φ, 0> | ||
+ | |||
+ | # x5o: | ||
+ | <-√((10+2*√5)/5), 0, -2*√((3-φ)/5)> | ||
+ | <-√((5-√5)/10), ±φ, -2*√((3-φ)/5)> | ||
+ | <√((5+2*√5)/5), ±1, -2*√((3-φ)/5)> | ||
+ | </pre> |
Revision as of 23:34, 23 May 2014
The pentagonal orthocupolarotunda is the 32nd Johnson solid. It can be constructed by gluing a pentagonal rotunda and a pentagonal cupola at their decagonal faces.
Coordinates
These coordinates give a pentagonal orthocupolarotunda having edge length 2, with its 5-fold axis of symmetry aligned to the Z-axis:
# x5o: <-√((10+2*√5)/5), 0, √((20+8*√5)/5)> <-√((5-√5)/10), ±φ, √((20+8*√5)/5)> < √((5+2*√5)/5), ±1, √((20+8*√5)/5)> # o5f: < √((20+8*√5)/5), 0, √((10+2*√5)/5)> <-√((25+11*√5)/10), ±φ, √((10+2*√5)/5)> < √((5+√5)/10), ±φ^2, √((10+2*√5)/5)> # x5x: <±√(3+4*φ), ±1, 0> <±√(2+φ), ±φ^2, 0> <0, ±2*φ, 0> # x5o: <-√((10+2*√5)/5), 0, -2*√((3-φ)/5)> <-√((5-√5)/10), ±φ, -2*√((3-φ)/5)> <√((5+2*√5)/5), ±1, -2*√((3-φ)/5)>