Acronym pedpy (alt.: pet), J13
Name pentagonal dipyramid,
(line-)pentagon-tegum
 
 © ©
Vertex figure [34], [35]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {3} (lacing):   arccos(-sqrt(5)/3) = 138.189685°
  • between {3} and {3} (equatorial):   arccos[(4 sqrt(5)-5)/15] = 74.754736°
Confer
related Johnson solids:
peppy  
variations:
co oo5ox&#zy (c = (5+3 sqrt(5))/5, y = sqrt[(6+2 sqrt(5))/5], ex derived)  
general polytopal classes:
Johnson solids   deltahedra   bistratic lace towers  
External
links
wikipedia   mathworld   quickfur  

Incidence matrix according to Dynkin symbol

oxo5ooo&#xt   → both heights = sqrt((5-sqrt(5))/10) = 0.525731
(pt || pseudo {5} || pt)

o..5o..    | 1 * * | 5 0 0 | 5 0
.o.5.o.    | * 5 * | 1 2 1 | 2 2
..o5..o    | * * 1 | 0 0 5 | 0 5
-----------+-------+-------+---
oo.5oo.&#x | 1 1 0 | 5 * * | 2 0
.x.5...    | 0 2 0 | * 5 * | 1 1
.oo5.oo&#x | 0 1 1 | * * 5 | 0 2
-----------+-------+-------+----
ox.5...&#x | 1 2 0 | 2 1 0 | 5 *
.xo5...&#x | 0 2 1 | 0 1 2 | * 5
or
o..5o..     & | 2 * |  5 0 |  5
.o.5.o.       | * 5 |  2 2 |  4
--------------+-----+------+---
oo.5oo.&#x  & | 1 1 | 10 * |  2
.x.5...       | 0 2 |  * 5 |  2
--------------+-----+------+---
ox.5...&#x  & | 1 2 |  2 1 | 10

yo ox5oo&#zx   → height = 0   (y = sqrt((10-2 sqrt(5))/5) = 1.051462)
(tegum product of line with {5})

o. o.5o.    | 2 * |  5 0 |  5
.o .o5.o    | * 5 |  2 2 |  4
------------+-----+------+---
oo oo5oo&#x | 1 1 | 10 * |  2
.. .x5.o    | 0 2 |  * 5 |  2
------------+-----+------+---
.. ox ..&#x | 1 2 |  2 1 | 10

© 2004-2018
top of page