Acronym	pedpedip
Name	pentadiminished pentagonal duoprism
	©   ©
Circumradius	sqrt[1+1/sqrt(5)] = 1.203002
Pattern	(based on the cut-open squares-torus of pedip)
Face vector	20, 60, 55, 15
Confer	uniform relative: pedip   general polytopal classes: isogonals
External links

Moving one edge length along one pentagon type of a pedip and a chord step corresponding to two edge steps along the orthogonal pentagon type, inscribes into pedip an internal chord of size y = sqrt(x²+f²) = sqrt[5+sqrt(5))/2] = 1.902113. Going on to do so, then produces a closing cirquit of 5 such edges, respectively vertices. It turns out, that these 5 out of 25 vertices of pedip describe a vertex inscribed y-pen. This in fact is a special instance of the stepprism construction. (The right picture highlights such an inscribed pentachoron within a pentagonal duoprism.) Esp. all vertices then could be encountered by an inscribed chiral compound of 5 such pens.

If one considers however only 4 such inscribed pens, the resulting hull polychoron is the in here described one. As it turns out it still remains isogonal. For sure it uses 3 different edge sizes: the remaining edges of size x = 1 (black in the pattern display), the new diagonals of the former squares with size q = sqrt(2) (red), and the chords of the former pentagons with size f = (1+sqrt(5))/2 (green).

©

It then has two cell types. One (yellow in the above net) is a bidiminishing of the former pedip cells (pip), which also occurs as the vertex figure polyhedron of spidrox, again shown at the very left, i.e. having their 2 reduced vertices each at maximal distance apart. The other (red) is the vertex figure polyhedron of pedip itself (situated underneath the here omitted vertices).

Incidence matrix

20 |  1  2  2  1 | 1  3  2  3 |  4 1
---+-------------+------------+-----
 2 | 10  *  *  * | 0  2  1  0 |  3 0  x (black)
 2 |  * 20  *  * | 1  1  1  0 |  3 0  x (black)
 2 |  *  * 20  * | 0  1  0  2 |  2 1  q (red)
 2 |  *  *  * 10 | 0  0  1  2 |  2 1  f (green)
---+-------------+------------+-----
 4 |  0  4  0  0 | 5  *  *  * |  2 0  x4o
 3 |  1  1  1  0 | * 20  *  * |  2 0  oq&#x (half square)
 4 |  1  2  0  1 | *  * 10  * |  2 0  xf&#x (dim. pentagon)
 3 |  0  0  2  1 | *  *  * 20 |  1 1  of&#q (sefa of pip)
---+-------------+------------+-----
 8 |  3  6  4  2 | 1  4  2  2 | 10 *  verf(spidrox)
 4 |  0  0  4  2 | 0  0  0  4 |  * 5  verf(pedip)