Acronym pesc (old: peppypy), K-4.86
Name pentagon scalene,
pentagon-pyramidal pyramid,
line atop fully orthogonal pentagon,
5 tet rosette
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
o5o           o5o
       o5x       
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dual (topologically selfdual, in different orientation)
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {5} between peppy and peppy:   144°
  • at {3} between peppy and tet:   arccos(sqrt[7+3 sqrt(5)]/4) = 22.238756°
Confer
uniform relative:
ex  
related segmentochora:
line || perp {n}   ikepy   pappy  
general polytopal classes:
segmentochora  

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


Incidence matrix according to Dynkin symbol

oox5ooo&#x   → height(1,2) = 1
               height(1,3) = height(2,3) = sqrt((5-sqrt(5))/10) = 0.525731

o.. o..    | 1 * *  1 5 0 0 | 5 5 0 0 | 5 1 0
.o. .o.    | * 1 *  1 0 5 0 | 5 0 5 0 | 5 0 1
..o ..o    | * * 5 | 0 1 1 2 | 1 2 2 1 | 2 1 1
-----------+-------+---------+---------+------
oo.5oo.&#x | 1 1 0 | 1 * * * | 5 0 0 0 | 5 0 0
o.o5o.o&#x | 1 0 1 | * 5 * * | 1 2 0 0 | 2 1 0
.oo5.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
-----------+-------+---------+---------+------
ooo5ooo&#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..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.x5o.o&#x  1 0 5 | 0 5 0 5 | 0 5 0 1 | * 1 *
.ox5.oo&#x  0 1 5 | 0 0 5 5 | 0 0 5 1 | * * 1

pt || peppy   → height = (sqrt(5)-1)/4 = 0.309017

o.. o..    | 1 * *  1 5 0 0 | 5 5 0 0 | 5 1 0
.o. .o.    | * 1 *  1 0 5 0 | 5 0 5 0 | 5 0 1
..o ..o    | * * 5 | 0 1 1 2 | 1 2 2 1 | 2 1 1
-----------+-------+---------+---------+------
oo.5oo.&#x | 1 1 0 | 1 * * * | 5 0 0 0 | 5 0 0
o.o5o.o&#x | 1 0 1 | * 5 * * | 1 2 0 0 | 2 1 0
.oo5.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
-----------+-------+---------+---------+------
ooo5ooo&#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..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.x5o.o&#x  1 0 5 | 0 5 0 5 | 0 5 0 1 | * 1 *
.ox5.oo&#x  0 1 5 | 0 0 5 5 | 0 0 5 1 | * * 1

line || perp {5}   → height = sqrt[(5-2 sqrt(5))/20] = 0.162460

o.. o..     & | 2 *  1  5 0 | 5  5 0 | 5 1
..o ..o       | * 5 | 0  2 2 | 1  4 1 | 2 2
--------------+-----+--------+--------+----
oo.5oo.&#x    | 2 0 | 1  * * | 5  0 0 | 5 0
o.o5o.o&#x  & | 1 1 | * 10 * | 1  2 0 | 2 1
..x ...       | 0 2 | *  * 5 | 0  2 1 | 1 2
--------------+-----+--------+--------+----
ooo5ooo&#x    | 2 1 | 1  2 0 | 5  * * | 2 0
o.x ...&#x  & | 1 2 | 0  2 1 | * 10 * | 1 1
..x5..o       | 0 5 | 0  0 5 | *  * 1 | 0 2
--------------+-----+--------+--------+----
oox ...&#x     2 2 | 1  4 1 | 2  2 0 | 5 *
o.x5o.o&#x  &  1 5 | 0  5 5 | 0  5 1 | * 2

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