Acronym ..., {5} || perp {5/2}
Name (degenerate) pentagon atop fully perpendicular pentagram,
pentagon-pentagram tegum
Circumradius ∞   i.e. flat in euclidean space
Confer
general polytopal classes:
decomposition  

It either can be thought of as a degenerate 5D segmentotope with zero height, or as a 4D tegum product of the formers bases.

As abstract polytope {5} || perp {5/2} is automorph, thereby just interchanging the roles of the bases.


Incidence matrix according to Dynkin symbol

ox5oo xo5/2oo&#x   → height = 0
({5} || perp {5/2})

o.5o. o.5/2o.    | 5 * | 2  5 0 | 1  5 10 0 | 1 10 5 | 2 5
.o5.o .o5/2.o    | * 5 | 0  5 2 | 0 10  5 1 | 5 10 1 | 5 2
-----------------+-----+--------+-----------+--------+----
.. .. x.   ..    | 2 0 | 5  * * | 1  0  5 0 | 0  5 5 | 1 5
oo5oo oo5/2oo&#x | 1 1 | * 25 * | 0  2  2 0 | 1  4 1 | 2 2
.x .. ..   ..    | 0 2 | *  * 5 | 0  5  0 1 | 5  5 0 | 5 1
-----------------+-----+--------+-----------+--------+----
.. .. x.5/2o.    | 5 0 | 5  0 0 | 1  *  * * | 0  0 5 | 0 5
ox .. ..   ..&#x | 1 2 | 0  2 1 | * 25  * * | 1  2 0 | 2 1
.. .. xo   ..&#x | 2 1 | 1  2 0 | *  * 25 * | 0  2 1 | 1 2
.x5.o ..   ..    | 0 5 | 0  0 5 | *  *  * 1 | 5  0 0 | 5 0
-----------------+-----+--------+-----------+--------+----
ox5oo ..   ..&#x  1 5 | 0  5 5 | 0  5  0 1 | 5  * * | 2 0
ox .. xo   ..&#x  2 2 | 1  4 1 | 0  2  2 0 | * 25 * | 1 1
.. .. xo5/2oo&#x  5 1 | 5  5 0 | 1  0  5 0 | *  * 5 | 0 2
-----------------+-----+--------+-----------+--------+----
ox5oo xo   ..&#x  2 5 | 1 10 5 | 0 10  5 1 | 2  5 0 | 5 *
ox .. xo5/2oo&#x  5 2 | 5 10 1 | 1  5 10 0 | 0  5 2 | * 5

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