Acronym	gike
TOCID symbol	J, s*O, s*TT
Name	great icosahedron, retrosnub tetrahedron, retrosnub tetratetrahedron
	© ©
Circumradius	sqrt[(5-sqrt(5))/8] = 0.587785
Inradius	sqrt[(7-3 sqrt(5))/24] = 0.485556
Vertex figure	[35]/2
General of army	ike
Colonel of regiment	sissid
Dual	gissid
Confer	Grünbaumian relatives: 2gike   gacid   sissid+2gike   2sissid+gike   sissid+3gike   3sissid+gike   2sissid+4gike   4sissid+2gike   compounds: sirsido   sirsei   segmentohedra: stappy   general polytopal classes: regular
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As abstract polytope gike is isomorphic to ike, thereby replacing vertex figure pentagrams by corresponding pentagons. – As such gike is a lieutenant.

Incidence matrix according to Dynkin symbol

o5/2o3x

.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o3x |  3 |  3 | 20

o5/3o3x

.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o3x |  3 |  3 | 20

x3/2o5/2o

.   .   . | 12 |  5 |  5
----------+----+----+---
x   .   . |  2 | 30 |  2
----------+----+----+---
x3/2o   . |  3 |  3 | 20

x3/2o5/3o

.   .   . | 12 |  5 |  5
----------+----+----+---
x   .   . |  2 | 30 |  2
----------+----+----+---
x3/2o   . |  3 |  3 | 20

s3/2s3/2s

demi( .   .   . ) | 12 | 1  2  2 | 1 1  3
------------------+----+---------+-------
      s   2   s   |  2 | 6  *  * | 0 0  2
sefa( s3/2s   . ) |  2 | * 12  * | 1 0  1
sefa( .   s3/2s ) |  2 | *  * 12 | 0 1  1
------------------+----+---------+-------
      s3/2s   .   ♦  3 | 0  3  0 | 4 *  *
      .   s3/2s   ♦  3 | 0  0  3 | * 4  *
sefa( s3/2s3/2s ) |  3 | 1  1  1 | * * 12

or
demi( .   .   . )                       | 12 | 1  4 | 2  3
----------------------------------------+----+------+-----
      s   2   s                         |  2 | 6  * | 0  2
sefa( s3/2s   . )  &  sefa( .   s3/2s ) |  2 | * 24 | 1  1
----------------------------------------+----+------+-----
      s3/2s   .    &        .   s3/2s   ♦  3 | 0  3 | 8  *
sefa( s3/2s3/2s )                       |  3 | 1  2 | * 12

s3/2s4o

demi( .   . . ) | 12 | 1  4 | 2  3
----------------+----+------+-----
      .   s4o   |  2 | 6  * | 0  2
sefa( s3/2s . ) |  2 | * 24 | 1  1
----------------+----+------+-----
      s3/2s .   ♦  3 | 0  3 | 8  *
sefa( s3/2s4o ) |  3 | 1  2 | * 12

s3/2s4/3o

demi( .   .   . ) | 12 | 1  4 | 2  3
------------------+----+------+-----
      .   s4/3o   |  2 | 6  * | 0  2
sefa( s3/2s   . ) |  2 | * 24 | 1  1
------------------+----+------+-----
      s3/2s   .   ♦  3 | 0  3 | 8  *
sefa( s3/2s4/3o ) |  3 | 1  2 | * 12