Acronym	pip
TOCID symbol	(5)P
Name	pentagonal prism, 5-p, vertex figure of rox
	© ©
Circumradius	sqrt[(15+2 sqrt(5))/20] = 0.986715
Vertex figure	[42,5] = of&#q
Volume	sqrt[25+10 sqrt(5)]/4 = 1.720477
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {4} and {4}:   108° between {4} and {5}:   90°
Face vector	10, 15, 7
Confer	general prisms: n-p   n/d-p   Grünbaumian relatives: 2pip   variations: q x5o   f x5o   v x5o   u x5o   x v5o   f v5o   compounds: kred   blends: 2-pip-blend   6-pip-blend   ambification: repip   general polytopal classes: Wythoffian polyhedra   ursatopes   segmentohedra   bistratic lace towers
External links

As abstract polytope pip is isomorphic to stip, thereby replacing pentagons by pentagrams.

Incidence matrix according to Dynkin symbol

x x5o

. . . | 10 | 1  2 | 2 1
------+----+------+----
x . . |  2 | 5  * | 2 0
. x . |  2 | * 10 | 1 1
------+----+------+----
x x . |  4 | 2  2 | 5 *
. x5o |  5 | 0  5 | * 2

snubbed forms: x2β5o, x2β5o (as mere faceting), β2β5o, β2β5o (as mere faceting)

x2s10o

demi( . .  . ) | 10 | 1  2 | 1 2
---------------+----+------+----
demi( x .  . ) |  2 | 5  * | 0 2
sefa( . s10o ) |  2 | * 10 | 1 1
---------------+----+------+----
      . s10o   |  5 | 0  5 | 2 *
sefa( x2s10o ) |  4 | 2  2 | * 5

starting figure: x x10o

x2s5s

demi( . . . ) | 10 | 1  2 | 1 2
--------------+----+------+----
demi( x . . ) |  2 | 5  * | 0 2
sefa( . s5s ) |  2 | * 10 | 1 1
--------------+----+------+----
      . s5s   |  5 | 0  5 | 2 *
sefa( x2s5s ) |  4 | 2  2 | * 5

starting figure: x x5x

xx5oo&#x   → height = 1
({5} || {5})

o.5o.    | 5 * | 2 1 0 | 1 2 0
.o5.o    | * 5 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 5 * * | 1 1 0
oo5oo&#x | 1 1 | * 5 * | 0 2 0
.x ..    | 0 2 | * * 5 | 0 1 1
---------+-----+-------+------
x.5o.    | 5 0 | 5 0 0 | 1 * *
xx ..&#x | 2 2 | 1 2 1 | * 5 *
.x5.o    | 0 5 | 0 0 5 | * * 1

xxx ofx&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057

o.. o..     | 2 * * | 1 2 0 0 0 0 | 2 1 0 0
.o. .o.     | * 4 * | 0 1 1 1 0 0 | 1 1 1 0
..o ..o     | * * 4 | 0 0 0 1 1 1 | 0 1 1 1
------------+-------+-------------+--------
x.. ...     | 2 0 0 | 1 * * * * * | 2 0 0 0
oo. oo.&#x  | 1 1 0 | * 4 * * * * | 1 1 0 0
.x. ...     | 0 2 0 | * * 2 * * * | 1 0 1 0
.oo .oo&#x  | 0 1 1 | * * * 4 * * | 0 1 1 0
..x ...     | 0 0 2 | * * * * 2 * | 0 0 1 1
... ..x     | 0 0 2 | * * * * * 2 | 0 1 0 1
------------+-------+-------------+--------
xx. ...&#x  | 2 2 0 | 1 2 1 0 0 0 | 2 * * *
... ofx&#xt | 1 2 2 | 0 2 0 2 0 1 | * 2 * *
.xx ...&#x  | 0 2 2 | 0 0 1 2 1 0 | * * 2 *
..x ..x     | 0 0 4 | 0 0 0 0 2 2 | * * * 1