Acronym prahi
Name prismatorhombated hecatonicosachoron,
runcitruncated hexacosachoron
Circumradius sqrt[35+15 sqrt(5)] = 8.278950
Vertex figure
 ©
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: grid hip pip saddid srid tut
spixady 12007201200600
prahi 012007200120600
& others)
Dihedral angles
  • at {6} between hip and tut:   arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756°
  • at {4} between hip and pip:   arccos(-sqrt[(10+2 sqrt(5))/15]) = 169.187683°
  • at {5} between pip and srid:   162°
  • at {4} between hip and srid:   arccos(-sqrt[(3+sqrt(5))/6]) = 159.094843°
  • at {3} between srid and tut:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244°
Confer
Grünbaumian relatives:
2prahi  
related CRFs:
sridagridtum  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope prahi is isomorphic to paqrigagishi, thereby replacing the pentagons by pentagrams, resp. replacing srid by qrid and replacing pip by stip.


Incidence matrix according to Dynkin symbol

x3x3o5x

. . . . | 7200 |    1    2    2 |    2    2    1    2    1 |   1    2   1   1
--------+------+----------------+--------------------------+-----------------
x . . . |    2 | 3600    *    * |    2    2    0    0    0 |   1    2   1   0
. x . . |    2 |    * 7200    * |    1    0    1    1    0 |   1    1   0   1
. . . x |    2 |    *    * 7200 |    0    1    0    1    1 |   0    1   1   1
--------+------+----------------+--------------------------+-----------------
x3x . . |    6 |    3    3    0 | 2400    *    *    *    * |   1    1   0   0
x . . x |    4 |    2    0    2 |    * 3600    *    *    * |   0    1   1   0
. x3o . |    3 |    0    3    0 |    *    * 2400    *    * |   1    0   0   1
. x . x |    4 |    0    2    2 |    *    *    * 3600    * |   0    1   0   1
. . o5x |    5 |    0    0    5 |    *    *    *    * 1440 |   0    0   1   1
--------+------+----------------+--------------------------+-----------------
x3x3o .    12 |    6   12    0 |    4    0    4    0    0 | 600    *   *   *
x3x . x    12 |    6    6    6 |    2    3    0    3    0 |   * 1200   *   *
x . o5x    10 |    5    0   10 |    0    5    0    0    2 |   *    * 720   *
. x3o5x    60 |    0   60   60 |    0    0   20   30   12 |   *    *   * 120

snubbed forms: β3x3o5x, x3β3o5x, x3x3o5β, β3β3o5x, β3x3o5β, x3β3o5β, β3β3o5β

x3x3/2o5/4x

. .   .   . | 7200 |    1    2    2 |    2    2    1    2    1 |   1    2   1   1
------------+------+----------------+--------------------------+-----------------
x .   .   . |    2 | 3600    *    * |    2    2    0    0    0 |   1    2   1   0
. x   .   . |    2 |    * 7200    * |    1    0    1    1    0 |   1    1   0   1
. .   .   x |    2 |    *    * 7200 |    0    1    0    1    1 |   0    1   1   1
------------+------+----------------+--------------------------+-----------------
x3x   .   . |    6 |    3    3    0 | 2400    *    *    *    * |   1    1   0   0
x .   .   x |    4 |    2    0    2 |    * 3600    *    *    * |   0    1   1   0
. x3/2o   . |    3 |    0    3    0 |    *    * 2400    *    * |   1    0   0   1
. x   .   x |    4 |    0    2    2 |    *    *    * 3600    * |   0    1   0   1
. .   o5/4x |    5 |    0    0    5 |    *    *    *    * 1440 |   0    0   1   1
------------+------+----------------+--------------------------+-----------------
x3x3/2o   .    12 |    6   12    0 |    4    0    4    0    0 | 600    *   *   *
x3x   .   x    12 |    6    6    6 |    2    3    0    3    0 |   * 1200   *   *
x .   o5/4x    10 |    5    0   10 |    0    5    0    0    2 |   *    * 720   *
. x3/2o5/4x    60 |    0   60   60 |    0    0   20   30   12 |   *    *   * 120

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