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°
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:
2pip-blend  
general polytopal classes:
ursatopes   segmentohedra   bistratic lace towers  
External
links
wikipedia   polytopewiki   WikiChoron   mathworld   quickfur

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, β2β5o

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

© 2004-2022
top of page