Pentagonal orthocupolarotunda (EntityTopic, 10)

From Hi.gher. Space

Revision as of 22:17, 4 September 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)>

Images