Acronym gad
TOCID symbol E
Name great dodecahedron,
vertex figure of fix
 
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Circumradius sqrt[(5+sqrt(5))/8] = 0.951057
Inradius sqrt[(5+sqrt(5))/40] = 0.425325
Density 3
Vertex figure [55]/2
Vertex layers
LayerSymmetrySubsymmetries
 o5o5/2oo5o   .o .   o. o5/2o
1x5o5/2oo5o   .x .   o
edge first
. o5/2o
vertex first
2x5o   .
{5} first
o .   f. f5/2o
vertex figure
3o5x   .
opposite {5}
f .   x. o5/2f
4o5o   .o .   f. o5/2o
opposite vertex
5 x .   o
opposite edge
 
Lace city
in approx. ASCII-art
 o   o 
   f   
x     x
   f   
 o   o 
Coordinates (τ/2, 1/2, 0)   & even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army ike
Colonel of regiment ike
Dual sissid
Dihedral angles
  • between {5} and {5}:   arccos(1/sqrt(5)) = 63.434949°
Confer
Grünbaumian relatives:
2gad   cid   ike+2gad   2ike+gad   ike+3gad   3ike+gad   3ike+3gad   4ike+gad   5ike+gad   2ike+4gad   4ike+2gad  
compounds:
presipsido   presipsi  
general polytopal classes:
regular   noble polytopes  
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   mathworld   nan ma

As abstract polytope gad is isomorphic to sissid, thereby replacing facial pentagons by pentagrams and conversely vertex figure pentagrams by corresponding pentagons. – As such gad is a lieutenant. Both gad and sissid can be seen as different realizations of the same self-dual regular abstract polyhedron {5,5}6 (where the index just denotes the size of the corresponding Petrie polygon).

This polyhedron is an edge-faceting of the icosahedron (ike).


Incidence matrix according to Dynkin symbol

o5/2o5x

.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o5x |  5 |  5 | 12

snubbed forms: o5/2o5β

o5/3o5x

.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o5x |  5 |  5 | 12

x5/4o5/2o

.   .   . | 12 |  5 |  5
----------+----+----+---
x   .   . |  2 | 30 |  2
----------+----+----+---
x5/4o   . |  5 |  5 | 12

x5/4o5/3o

.   .   . | 12 |  5 |  5
----------+----+----+---
x   .   . |  2 | 30 |  2
----------+----+----+---
x5/4o   . |  5 |  5 | 12

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