Acronym	...
Name	edge faceting raded-1-10-5-5
VRML	⭳
Circumradius	sqrt(7)/2 = 1.322876
Vertex figure	[4,5,6], [4,5,4,5/2], [4,6,4/3,6/5]/0
Face vector	30, 50, 21
Confer	faceting of: raded   blends: 12 raded-1-10-5-5
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By inspectation from the open end, it becomes visible that the central part of the pentagram here is a membran only: it is accessible from both sides.

It should be noted here, that the squares are situated fully within the mirror planes underneath the edges of doe. Accordingly there could be constructed an (centrally hollow) external blend from 12 such self-intersecting polyhedra (12 raded-1-10-5-5), blending out half of their squares, cf. the picture at the right.

Incidence matrix according to Dynkin symbol

reduced( xxux5/2ofxx&#xt , by {10/2} )   → height(1,2) = sqrt[(5-sqrt(5))/10] = 0.525731
                                           height(2,3) = sqrt[(9 sqrt(5)-15)/10] = 0.715864
                                           height(3,4) = sqrt[(5+sqrt(5))/10] = 0.850651

o...5/2o...      | 5  *  * * | 2  2 0  0 0  0 0 | 1 2 1 0 0  [4,5,4,5/2]
.o..5/2.o..      | * 10  * * | 0  1 1  1 0  0 0 | 0 1 1 1 0  [4,5,6]
..o.5/2..o.      | *  * 10 * | 0  0 0  1 1  1 0 | 0 0 1 1 1  [4,5,6]
...o5/2...o      | *  *  * 5 | 0  0 0  0 0  2 2 | 0 0 0 2 2  [4,6,4/3,6/5]/0
-----------------+-----------+------------------+----------
x...   ....      | 2  0  0 0 | 5  * *  * *  * * | 1 1 0 0 0
oo..5/2oo..&#x   | 1  1  0 0 | * 10 *  * *  * * | 0 1 1 0 0
.x..   ....      | 0  2  0 0 | *  * 5  * *  * * | 0 1 0 1 0
.oo.5/2.oo.&#x   | 0  1  1 0 | *  * * 10 *  * * | 0 0 1 1 0
....   ..x.      | 0  0  2 0 | *  * *  * 5  * * | 0 0 1 0 1
..oo5/2..oo&#x   | 0  0  1 1 | *  * *  * * 10 * | 0 0 0 1 1
...x   ....    & | 0  0  0 2 | *  * *  * *  * 5 | 0 0 0 1 1
-----------------+-----------+------------------+----------
x...5/2o...      | 5  0  0 0 | 5  0 0  0 0  0 0 | 1 * * * *
xx..   ....&#x   | 2  2  0 0 | 1  2 1  0 0  0 0 | * 5 * * *
....   ofx.&#xt  | 1  2  2 0 | 0  2 0  2 1  0 0 | * * 5 * *
.xux   ....&#xt  | 0  2  2 2 | 0  0 1  2 0  2 1 | * * * 5 *
....   ..xx&#x   | 0  0  2 2 | 0  0 0  0 1  2 1 | * * * * 5