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°
Face vector	7, 16, 16, 7
Confer	uniform relative: ex   related segmentochora: line || perp {n}   ikepy   pappy   general polytopal classes: segmentochora   scalene
External links

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

pyramid product of line with {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