Acronym stasc (old: stappypy)
Name stellar scalene,
pentagram-scalene,
pentagram-pyramidal pyramid,
line atop fully orthogonal pentagram,
5 tet two-step rosette
Circumradius (sqrt(5)-1)/2 = 0.618034
Dual (topologically selfdual, in different orientation)
Dihedral angles
  • at {3} between stappy and tet:   arccos(sqrt[7-3 sqrt(5)]/4) = 82.238756°
  • at {5/2} between stappy and stappy:   72°
  • at {3} between tet and tet:   arccos[(3 sqrt(5)-1)/8] = 44.477512°
Confer
uniform relative:
gax  
segmentochora:
gikepy  
general polytopal classes:
segmentochora  

As abstract polytope stasc is isomorphic to pesc, thereby replacing pentagrams by pentagons resp. replacing stappy by peppy.


Incidence matrix according to Dynkin symbol

oox5/2ooo&#x   → height(1,2) = 1
                 height(1,3) = height(2,3) = sqrt((5+sqrt(5))/10) = 0.850651

o..5/2o..    | 1 * *  1 4 0 0 | 4 4 0 0 | 4 1 0
.o.5/2.o.    | * 1 *  1 0 4 0 | 4 0 4 0 | 4 0 1
..o5/2..o    | * * 5 | 0 1 1 2 | 1 2 2 1 | 2 1 1
-------------+-------+---------+---------+------
oo.5/2oo.&#x | 1 1 0 | 1 * * * | 5 0 0 0 | 5 0 0
o.o5/2o.o&#x | 1 0 1 | * 5 * * | 1 2 0 0 | 2 1 0
.oo5/2.oo&#x | 0 1 1 | * * 5 * | 1 0 2 0 | 2 0 1
..x   ...    | 0 0 2 | * * * 5 | 0 1 1 1 | 1 1 1
-------------+-------+---------+---------+------
ooo5/2ooo&#x | 1 1 1 | 1 1 1 0 | 5 * * * | 2 0 0
o.x   ...&#x | 1 0 2 | 0 2 0 1 | * 5 * * | 1 1 0
.ox   ...&#x | 0 1 2 | 0 0 2 1 | * * 5 * | 1 0 1
..x5/2..o    | 0 0 5 | 0 0 0 5 | * * * 1 | 0 1 1
-------------+-------+---------+---------+------
oox   ...&#x  1 1 2 | 1 2 2 1 | 2 1 1 0 | 5 * *
o.x5/2o.o&#x  1 0 5 | 0 5 0 5 | 0 5 0 1 | * 1 *
.ox5/2.oo&#x  0 1 5 | 0 0 5 5 | 0 0 5 1 | * * 1

pt || stappy   → height = (1+sqrt(5))/4 = 0.809017

o..5/2o..    | 1 * *  1 4 0 0 | 4 4 0 0 | 4 1 0
.o.5/2.o.    | * 1 *  1 0 4 0 | 4 0 4 0 | 4 0 1
..o5/2..o    | * * 5 | 0 1 1 2 | 1 2 2 1 | 2 1 1
-------------+-------+---------+---------+------
oo.5/2oo.&#x | 1 1 0 | 1 * * * | 5 0 0 0 | 5 0 0
o.o5/2o.o&#x | 1 0 1 | * 5 * * | 1 2 0 0 | 2 1 0
.oo5/2.oo&#x | 0 1 1 | * * 5 * | 1 0 2 0 | 2 0 1
..x   ...    | 0 0 2 | * * * 5 | 0 1 1 1 | 1 1 1
-------------+-------+---------+---------+------
ooo5/2ooo&#x | 1 1 1 | 1 1 1 0 | 5 * * * | 2 0 0
o.x   ...&#x | 1 0 2 | 0 2 0 1 | * 5 * * | 1 1 0
.ox   ...&#x | 0 1 2 | 0 0 2 1 | * * 5 * | 1 0 1
..x5/2..o    | 0 0 5 | 0 0 0 5 | * * * 1 | 0 1 1
-------------+-------+---------+---------+------
oox   ...&#x  1 1 2 | 1 2 2 1 | 2 1 1 0 | 5 * *
o.x5/2o.o&#x  1 0 5 | 0 5 0 5 | 0 5 0 1 | * 1 *
.ox5/2.oo&#x  0 1 5 | 0 0 5 5 | 0 0 5 1 | * * 1

line || perp {5/2}   → height = sqrt[(5+2 sqrt(5))/20] = 0.688191

o..5/2o..     & | 2 *  1  4 0 | 4  4 0 | 4 1
..o5/2..o       | * 5 | 0  2 2 | 1  4 1 | 2 2
----------------+-----+--------+--------+----
oo.5/2oo.&#x    | 2 0 | 1  * * | 5  0 0 | 5 0
o.o5/2o.o&#x  & | 1 1 | * 10 * | 1  2 0 | 2 1
..x   ...       | 0 2 | *  * 5 | 0  2 1 | 1 2
----------------+-----+--------+--------+----
ooo5/2ooo&#x    | 2 1 | 1  2 0 | 5  * * | 2 0
o.x   ...&#x  & | 1 2 | 0  2 1 | * 10 * | 1 1
..x5/2..o       | 0 5 | 0  0 5 | *  * 1 | 0 2
----------------+-----+--------+--------+----
oox   ...&#x     2 2 | 1  4 1 | 2  2 0 | 5 *
o.x5/2o.o&#x  &  1 5 | 0  5 5 | 0  5 1 | * 2

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