Acronym aud, J58
Name augmented dodecahedron
 
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Vertex figures [35], [32,52], [53]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {5}:   arccos(-sqrt[(65-2 sqrt(5))/75]) = 153.942419°
  • between {3} and {3}:   arccos(-sqrt(5)/3) = 138.189685°
  • between {5} and {5}:   arccos(-1/sqrt(5)) = 116.565051°
Confer
uniform relatives:
doe   ike  
related Johnson solids:
peppy   mabaud   pabaud  
general polytopal classes:
Johnson solids  
External
links
wikipedia   mathworld

Incidence matrix according to Dynkin symbol

oxfoo5ooofx&#xt   → height(1,2) = height(3,4) = sqrt((5-sqrt(5))/10) = 0.525731
                    height(2,3) = height(4,5) = sqrt[(5+sqrt(5))/10] = 0.850651
(pt || pseudo {5} || pseudo f-{5} || pseudo dual f-{5} || dual {5})

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

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