Pentagonal orthocupolarotunda pseudopyramid (EntityTopic, 14)

From Hi.gher. Space

The pentagonal orthocupolarotunda pseudopyramid, or J32 pseudopyramid, is a 4D CRF polytope that has a pentagonal orthocupolarotunda base and a pentagonal apex, laced by 5 pentagonal pyramids, 10 square pyramids, 5 triangular prisms, 5 tetrahedra, and 2 pentagonal prisms. It can be denoted as J32 || pentagon in Klitzing's notation.

Projections

Centered on pentagonal apex:

Coordinates

<-√((10+2*√5)/5), 0,    √((20+8*√5)/5), 0>
<-√((5-√5)/10),   ±phi, √((20+8*√5)/5), 0>
< √((5+2*√5)/5),  ±1,   √((20+8*√5)/5), 0>

< √((20+8*√5)/5),   0,      √((10+2*√5)/5), 0>
<-√((25+11*√5)/10), ±phi,   √((10+2*√5)/5), 0>
< √((5+√5)/10),     ±phi^2, √((10+2*√5)/5), 0>

<±√(3+4*phi), ±1,     0, 0>
<±√(2+phi),   ±phi^2, 0, 0>
<0,           ±2*phi, 0, 0>

<-√((10+2*√5)/5), 0,    -2*√((3-phi)/5), 0>
<-√((5-√5)/10),   ±phi, -2*√((3-phi)/5), 0>
< √((5+2*√5)/5),  ±1,   -2*√((3-phi)/5), 0>

<-√((10+2*√5)/5), 0,    √((2+phi)/5), 1/phi>
<-√((5-√5)/10),   ±phi, √((2+phi)/5), 1/phi>
<√((5+2*√5)/5),   ±1,   √((2+phi)/5), 1/phi>

where phi = (1+√5)/2 is the Golden Ratio.

Software models

• Polyview .def file
• Stella4d .off file