Acronym ipe, K-4.36
Name icosahedron prism,
vertex figure of rectified hyperbolic pentachoric honeycomb
Segmentochoron display
Cross sections 
 ©
Circumradius sqrt[(7+sqrt(5))/8] = 1.074481
General of army (is itself convex)
Colonel of regiment (is itself locally convex – other uniform polychoral member: gaddip)
Dihedral angles
  • at {4} between trip and trip:   arccos(-sqrt(5)/3) = 138.189685°
  • at {3} between ike and trip:   90°
Face vector 24, 72, 70, 22
Confer
related segmentochora:
peppyp  
general polytopal classes:
Wythoffian polychora   segmentochora  
External
links 		hedrondude   wikipedia   polytopewiki

As abstract polytope ipe is isomorphic to gipe, thereby replacing ike by gike.


Incidence matrix according to Dynkin symbol

x x3o5o

. . . . | 24 |  1  5 |  5  5 |  5 1
--------+----+-------+-------+-----
x . . . |  2 | 12  * |  5  0 |  5 0
. x . . |  2 |  * 60 |  1  2 |  2 1
--------+----+-------+-------+-----
x x . . |  4 |  2  2 | 30  * |  2 0
. x3o . |  3 |  0  3 |  * 40 |  1 1
--------+----+-------+-------+-----
x x3o . ♦  6 |  3  6 |  3  2 | 20 *
. x3o5o ♦ 12 |  0 30 |  0 20 |  * 2


x x3o5/4o

. . .   . | 24 |  1  5 |  5  5 |  5 1
----------+----+-------+-------+-----
x . .   . |  2 | 12  * |  5  0 |  5 0
. x .   . |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x x .   . |  4 |  2  2 | 30  * |  2 0
. x3o   . |  3 |  0  3 |  * 40 |  1 1
----------+----+-------+-------+-----
x x3o   . ♦  6 |  3  6 |  3  2 | 20 *
. x3o5/4o ♦ 12 |  0 30 |  0 20 |  * 2


x x3/2o5o

. .   . . | 24 |  1  5 |  5  5 |  5 1
----------+----+-------+-------+-----
x .   . . |  2 | 12  * |  5  0 |  5 0
. x   . . |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x x   . . |  4 |  2  2 | 30  * |  2 0
. x3/2o . |  3 |  0  3 |  * 40 |  1 1
----------+----+-------+-------+-----
x x3/2o . ♦  6 |  3  6 |  3  2 | 20 *
. x3/2o5o ♦ 12 |  0 30 |  0 20 |  * 2


x x3/2o5/4o

. .   .   . | 24 |  1  5 |  5  5 |  5 1
------------+----+-------+-------+-----
x .   .   . |  2 | 12  * |  5  0 |  5 0
. x   .   . |  2 |  * 60 |  1  2 |  2 1
------------+----+-------+-------+-----
x x   .   . |  4 |  2  2 | 30  * |  2 0
. x3/2o   . |  3 |  0  3 |  * 40 |  1 1
------------+----+-------+-------+-----
x x3/2o   . ♦  6 |  3  6 |  3  2 | 20 *
. x3/2o5/4o ♦ 12 |  0 30 |  0 20 |  * 2


x s3s4o

. demi( . . . ) | 24 |  1  1  4 | 1  4  2  3 | 2  3 1
----------------+----+----------+------------+-------
x demi( . . . ) |  2 | 12  *  * | 1  4  0  0 | 2  3 0
.       . s4o   |  2 |  * 12  * | 1  0  0  2 | 0  2 1
. sefa( s3s . ) |  2 |  *  * 48 | 0  1  1  1 | 1  1 1
----------------+----+----------+------------+-------
x       . s4o   |  4 |  2  2  0 | 6  *  *  * | 0  2 0
x sefa( s3s . ) ♦  4 |  2  0  2 | * 24  *  * | 1  1 0
.       s3s .   ♦  3 |  0  0  3 | *  * 16  * | 1  0 1
. sefa( s3s4o ) |  3 |  0  1  2 | *  *  * 24 | 0  1 1
----------------+----+----------+------------+-------
x       s3s .   ♦  6 |  3  0  6 | 0  3  2  0 | 8  * *
x sefa( s3s4o ) ♦  6 |  3  2  4 | 1  2  0  2 | * 12 *
.       s3s4o   ♦ 12 |  0  6 24 | 0  0  8 12 | *  * 2


x s3s3s

. demi( . . . ) | 24 |  1  1  2  2 | 1  2  2 1 1  3 | 1 1  3 1
----------------+----+-------------+----------------+---------
x demi( . . . ) |  2 | 12  *  *  * | 1  2  2 0 0  0 | 1 1  3 0
.       s 2 s   |  2 |  * 12  *  * | 1  0  0 0 0  2 | 0 0  2 1
. sefa( s3s . ) |  2 |  *  * 24  * | 0  1  0 1 0  1 | 1 0  1 1
. sefa( . s3s ) |  2 |  *  *  * 24 | 0  0  1 0 1  1 | 0 1  1 1
----------------+----+-------------+----------------+---------
x       s 2 s   |  4 |  2  2  0  0 | 6  *  * * *  * | 0 0  2 0
x sefa( s3s . ) |  4 |  2  0  2  0 | * 12  * * *  * | 1 0  1 0
x sefa( . s3s ) |  4 |  2  0  0  2 | *  * 12 * *  * | 0 1  1 0
.       s3s .   ♦  3 |  0  0  3  0 | *  *  * 8 *  * | 1 0  0 1
.       . s3s   ♦  3 |  0  0  0  3 | *  *  * * 8  * | 0 1  0 1
. sefa( s3s3s ) |  3 |  0  1  1  1 | *  *  * * * 24 | 0 0  1 1
----------------+----+-------------+----------------+---------
x       s3s .   ♦  6 |  3  0  6  0 | 0  3  0 2 0  0 | 4 *  * *
x       . s3s   ♦  6 |  3  0  0  6 | 0  0  3 0 2  0 | * 4  * *
x sefa( s3s3s ) ♦  6 |  3  2  2  2 | 1  1  1 0 0  2 | * * 12 *
.       s3s3s   ♦ 12 |  0  6 12 12 | 0  0  0 4 4 12 | * *  * 2


x2s3s4o

demi( . . . . ) | 24 |  1  1  4 | 1  2  4  3 | 2 1  3
----------------+----+----------+------------+-------
demi( x . . . ) |  2 | 12  *  * | 1  0  4  0 | 2 0  3
      . . s4o   |  2 |  * 12  * | 1  0  0  2 | 0 1  2
sefa( . s3s . ) |  2 |  *  * 48 | 0  1  1  1 | 1 1  1
----------------+----+----------+------------+-------
      x 2 s4o   |  4 |  2  2  0 | 6  *  *  * | 0 0  2
      . s3s .   ♦  3 |  0  0  3 | * 16  *  * | 1 1  0
sefa( x2s3s . ) ♦  4 |  2  0  2 | *  * 24  * | 1 0  1
sefa( . s3s4o ) |  3 |  0  1  2 | *  *  * 24 | 0 1  1
----------------+----+----------+------------+-------
      x2s3s .   ♦  6 |  3  0  6 | 0  2  3  0 | 8 *  *
      . s3s4o   ♦ 12 |  0  6 24 | 0  8  0 12 | * 2  *
sefa( x2s3s4o ) ♦  6 |  3  2  4 | 1  0  2  2 | * * 12

starting figure: x x3x4o


x2s3s3s

demi( . . . . ) | 24 |  1  1  2  2 | 1 1 1  2  2  3 | 1 1 1  3
----------------+----+-------------+----------------+---------
demi( x . . . ) |  2 | 12  *  *  * | 1 0 0  2  2  0 | 1 1 0  3
      . s 2 s   |  2 |  * 12  *  * | 1 0 0  0  0  2 | 0 0 1  2
sefa( . s3s . ) |  2 |  *  * 24  * | 0 1 0  1  0  1 | 1 0 1  1
sefa( . . s3s ) |  2 |  *  *  * 24 | 0 0 1  0  1  1 | 0 1 1  1
----------------+----+-------------+----------------+---------
      x2s 2 s   |  4 |  2  2  0  0 | 6 * *  *  *  * | 0 0 0  2
      . s3s .   ♦  3 |  0  0  3  0 | * 8 *  *  *  * | 1 0 1  0
      . . s3s   ♦  3 |  0  0  0  3 | * * 8  *  *  * | 0 1 1  0
sefa( x2s3s . ) |  4 |  2  0  2  0 | * * * 12  *  * | 1 0 0  1
sefa( x 2 s3s ) |  4 |  2  0  0  2 | * * *  * 12  * | 0 1 0  1
sefa( . s3s3s ) |  3 |  0  1  1  1 | * * *  *  * 24 | 0 0 1  1
----------------+----+-------------+----------------+---------
      x2s3s .   ♦  6 |  3  0  6  0 | 0 2 0  3  0  0 | 4 * *  *
      x 2 s3s   ♦  6 |  3  0  0  6 | 0 0 2  0  3  0 | * 4 *  *
      . s3s3s   ♦ 12 |  0  6 12 12 | 0 4 4  0  0 12 | * * 2  *
sefa( x2s3s3s ) ♦  6 |  3  2  2  2 | 1 0 0  1  1  2 | * * * 12

starting figure: x x3x3x


xx3oo5oo&#x   → height = 1
(ike || ike)

o.3o.5o.    | 12  * |  5  1  0 |  5  5  0 | 1  5 0
.o3.o5.o    |  * 12 |  0  1  5 |  0  5  5 | 0  5 1
------------+-------+----------+----------+-------
x. .. ..    |  2  0 | 30  *  * |  2  1  0 | 1  2 0
oo3oo5oo&#x |  1  1 |  * 12  * |  0  5  0 | 0  5 0
.x .. ..    |  0  2 |  *  * 30 |  0  1  2 | 0  2 1
------------+-------+----------+----------+-------
x.3o. ..    |  3  0 |  3  0  0 | 20  *  * | 1  1 0
xx .. ..&#x |  2  2 |  1  2  1 |  * 30  * | 0  2 0
.x3.o ..    |  0  3 |  0  0  3 |  *  * 20 | 0  1 1
------------+-------+----------+----------+-------
x.3o.5o.    ♦ 12  0 | 30  0  0 | 20  0  0 | 1  * *
xx3oo ..&#x ♦  3  3 |  3  3  3 |  1  3  1 | * 20 *
.x3.o5.o    ♦  0 12 |  0  0 30 |  0  0 20 | *  * 1


s3s3s || s3s3s   → height = 1
(ike || ike)

demi( . . . )                 | 12  * | 1  2  2  1 0  0  0 | 1 1  3 1  2  2 0 0  0 | 1 1 1  3 0
                demi( . . . ) |  * 12 | 0  0  0  1 1  2  2 | 0 0  0 1  2  2 1 1  3 | 0 1 1  3 1
------------------------------+-------+--------------------+-----------------------+-----------
      s 2 s                   |  2  0 | 6  *  *  * *  *  * | 0 0  2 1  0  0 0 0  0 | 1 0 0  2 0
sefa( s3s . )                 |  2  0 | * 12  *  * *  *  * | 1 0  1 0  1  0 0 0  0 | 1 1 0  1 0
sefa( . s3s )                 |  2  0 | *  * 12  * *  *  * | 0 1  1 0  0  1 0 0  0 | 1 0 1  1 0
demi( . . . ) || demi( . . . ) |  1  1 | *  *  * 12 *  *  * | 0 0  0 1  2  2 0 0  0 | 0 1 1  3 0
                      s 2 s   |  0  2 | *  *  *  * 6  *  * | 0 0  0 1  0  0 0 0  2 | 0 0 0  2 1
                sefa( s3s . ) |  0  2 | *  *  *  * * 12  * | 0 0  0 0  1  0 1 0  1 | 0 1 0  1 1
                sefa( . s3s ) |  0  2 | *  *  *  * *  * 12 | 0 0  0 0  0  1 0 1  1 | 0 0 1  1 1
------------------------------+-------+--------------------+-----------------------+-----------
      s3s .                   ♦  3  0 | 0  3  0  0 0  0  0 | 4 *  * *  *  * * *  * | 1 1 0  0 0
      . s3s                   ♦  3  0 | 0  0  3  0 0  0  0 | * 4  * *  *  * * *  * | 1 0 1  0 0
sefa( s3s3s )                 |  3  0 | 1  1  1  0 0  0  0 | * * 12 *  *  * * *  * | 1 0 0  1 0
      s 2 s   ||       s 2 s   |  2  2 | 1  0  0  2 1  0  0 | * *  * 6  *  * * *  * | 0 0 0  2 0
sefa( s3s . ) || sefa( s3s . ) |  2  2 | 0  1  0  2 0  1  0 | * *  * * 12  * * *  * | 0 1 0  1 0
sefa( . s3s ) || sefa( . s3s ) |  2  2 | 0  0  1  2 0  0  1 | * *  * *  * 12 * *  * | 0 0 1  1 0
                      s3s .   ♦  0  3 | 0  0  0  0 0  3  0 | * *  * *  *  * 4 *  * | 0 1 0  0 1
                      . s3s   ♦  0  3 | 0  0  0  0 0  0  3 | * *  * *  *  * * 4  * | 0 0 1  0 1
                sefa( s3s3s ) |  0  3 | 0  0  0  0 1  1  1 | * *  * *  *  * * * 12 | 0 0 0  1 1
------------------------------+-------+--------------------+-----------------------+-----------
      s3s3s                   ♦ 12  0 | 6 12 12  0 0  0  0 | 4 4 12 0  0  0 0 0  0 | 1 * *  * *
      s3s .   ||       s3s .   ♦  3  3 | 0  3  0  3 0  3  0 | 1 0  0 0  3  0 1 0  0 | * 4 *  * *
      . s3s   ||       . s3s   ♦  3  3 | 0  0  3  3 0  0  3 | 0 1  0 0  0  3 0 1  0 | * * 4  * *
sefa( s3s3s ) || sefa( s3s3s ) ♦  3  3 | 1  1  1  3 1  1  1 | 0 0  1 1  1  1 0 0  1 | * * * 12 *
                      s3s3s   ♦  0 12 | 0  0  0  0 6 12 12 | 0 0  0 0  0  0 4 4 12 | * * *  * 1

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