Pentagonal orthocupolarotunda (EntityTopic, 10)

From Hi.gher. Space

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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.
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==Coordinates==
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These coordinates give a pentagonal orthocupolarotunda having edge length 2, with its 5-fold axis of symmetry aligned to the Z-axis:
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<pre>
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# x5o:
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<-√((10+2*√5)/5), 0,    √((20+8*√5)/5)>
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<-√((5-√5)/10),  ±φ, √((20+8*√5)/5)>
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< √((5+2*√5)/5),  ±1,  √((20+8*√5)/5)>
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# o5f:
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< √((20+8*√5)/5),  0,      √((10+2*√5)/5)>
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<-√((25+11*√5)/10), ±φ,  √((10+2*√5)/5)>
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< √((5+√5)/10),    ±φ^2, √((10+2*√5)/5)>
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# x5x:
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<±√(3+4*φ), ±1,    0>
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<±√(2+φ),  ±φ^2, 0>
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<0,          ±2*φ, 0>
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# x5o:
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<-√((10+2*√5)/5), 0,    -2*√((3-φ)/5)>
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<-√((5-√5)/10),  ±φ, -2*√((3-φ)/5)>
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<√((5+2*√5)/5),  ±1,  -2*√((3-φ)/5)>
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</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)>