Acronym pobro, J34
Name pentagonal orthobirotunda
 
 © ©
Circumradius (1+sqrt(5))/2 = 1.618034
Vertex figure [(3,5)2], [32,52]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {3}:   arccos(-(5+4 sqrt(5))/15) = 158.375366°
  • between {3} and {5}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • between {5} and {5}:   arccos(-3/5) = 126.869898°
Confer
uniform relative:
id  
related Johnson solids:
pero   epobro  
general polytopal classes:
Johnson solids  
External
links
wikipedia   mathworld   quickfur  

Incidence matrix according to Dynkin symbol

xoxox5ofxfo&#xt   → outer heights = sqrt[(5-sqrt(5))/10] = 0.525731
                    inner heights = sqrt[(5+sqrt(5))/10] = 0.850651
({5} || pseudo dual f-{5} || pseudo {10} || pseudo dual f-{5} || {5})

o....5o....     | 5 *  * * * | 2  2  0 0 0  0  0 0 | 1 2 1 0 0 0 0 0
.o...5.o...     | * 5  * * * | 0  2  2 0 0  0  0 0 | 0 1 2 1 0 0 0 0
..o..5..o..     | * * 10 * * | 0  0  1 1 1  1  0 0 | 0 0 1 1 1 1 0 0
...o.5...o.     | * *  * 5 * | 0  0  0 0 0  2  2 0 | 0 0 0 0 1 2 1 0
....o5....o     | * *  * * 5 | 0  0  0 0 0  0  2 2 | 0 0 0 0 0 1 2 1
----------------+------------+---------------------+----------------
x.... .....     | 2 0  0 0 0 | 5  *  * * *  *  * * | 1 1 0 0 0 0 0 0
oo...5oo...&#x  | 1 1  0 0 0 | * 10  * * *  *  * * | 0 1 1 0 0 0 0 0
.oo..5.oo..&#x  | 0 1  1 0 0 | *  * 10 * *  *  * * | 0 0 1 1 0 0 0 0
..x.. .....     | 0 0  2 0 0 | *  *  * 5 *  *  * * | 0 0 0 1 1 0 0 0
..... ..x..     | 0 0  2 0 0 | *  *  * * 5  *  * * | 0 0 1 0 0 1 0 0
..oo.5..oo.&#x  | 0 0  1 1 0 | *  *  * * * 10  * * | 0 0 0 0 1 1 0 0
...oo5...oo&#x  | 0 0  0 1 1 | *  *  * * *  * 10 * | 0 0 0 0 0 1 1 0
....x .....     | 0 0  0 0 2 | *  *  * * *  *  * 5 | 0 0 0 0 0 0 1 1
----------------+------------+---------------------+----------------
x....5o....     | 5 0  0 0 0 | 5  0  0 0 0  0  0 0 | 1 * * * * * * *
xo... .....&#x  | 2 1  0 0 0 | 1  2  0 0 0  0  0 0 | * 5 * * * * * *
..... ofx..&#xt | 1 2  2 0 0 | 0  2  2 0 1  0  0 0 | * * 5 * * * * *
.ox.. .....&#x  | 0 1  2 0 0 | 0  0  2 1 0  0  0 0 | * * * 5 * * * *
..xo. .....&#x  | 0 0  2 1 0 | 0  0  0 1 0  2  0 0 | * * * * 5 * * *
..... ..xfo&#xt | 0 0  2 2 1 | 0  0  0 0 1  2  2 0 | * * * * * 5 * *
...ox .....&#x  | 0 0  0 1 2 | 0  0  0 0 0  0  2 1 | * * * * * * 5 *
....x5....o     | 0 0  0 0 5 | 0  0  0 0 0  0  0 5 | * * * * * * * 1
or
o....5o....      & | 10  *  * |  2  2  0 0 0 | 1  2  1  0
.o...5.o...      & |  * 10  * |  0  2  2 0 0 | 0  1  2  1
..o..5..o..        |  *  * 10 |  0  0  2 1 1 | 0  0  2  2
-------------------+----------+--------------+-----------
x.... .....      & |  2  0  0 | 10  *  * * * | 1  1  0  0
oo...5oo...&#x   & |  1  1  0 |  * 20  * * * | 0  1  1  0
.oo..5.oo..&#x   & |  0  1  1 |  *  * 20 * * | 0  0  1  1
..x.. .....        |  0  0  2 |  *  *  * 5 * | 0  0  0  2
..... ..x..        |  0  0  2 |  *  *  * * 5 | 0  0  2  0
-------------------+----------+--------------+-----------
x....5o....      & |  5  0  0 |  5  0  0 0 0 | 2  *  *  *
xo... .....&#x   & |  2  1  0 |  1  2  0 0 0 | * 10  *  *
..... ofx..&#xt  & |  1  2  2 |  0  2  2 0 1 | *  * 10  *
.ox.. .....&#x   & |  0  1  2 |  0  0  2 1 0 | *  *  * 10

© 2004-2018
top of page