Acronym tan
Name truncated penteract
Field of sections
 ©
Circumradius sqrt[13+8 sqrt(2)]/2 = 2.465447
Inradius
wrt. tat
[1+sqrt(2)]/2 = 1.207107
Inradius
wrt. pen
(5+4 sqrt(2))/sqrt(20) = 2.382945
Vertex figure
 ©    ©
Lace city
in approx. ASCII-art
 ©  
o3x4x  o3o4w    o3o4w  o3x4x		-- o3o3x4x (tat)
                            
                            
                            
o3o4w                  o3o4w		-- o3o3o4w (w-tes)
                            
                            
                            
                            
o3o4w                  o3o4w		-- o3o3o4w (w-tes)
                            
                            
                            
o3x4x  o3o4w    o3o4w  o3x4x		-- o3o3x4x (tat)
Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
Volume (1230+869 sqrt(2))/30 = 81.965053
Surface (505+360 sqrt(2)+sqrt(5))/3 = 338.784317
Dihedral angles
(at margins)
  • at tet between pen and tat:   arccos[-1/sqrt(5)] = 116.565051°
  • at tic between tat and tat:   90°
Confer
analogs:
truncated hypercube tCn  
External
links
hedrondude   wikipedia   polytopewiki  

As abstract polytope tan is isomorphic to quittin, thereby replacing octagons by octagrams, resp. tic by quith, resp. tat by quitit.


Incidence matrix according to Dynkin symbol

o3o3o3x4x

. . . . . | 160 |   4  1 |   6  4 |   4  6 |  1  4
----------+-----+--------+--------+--------+------
. . . x . |   2 | 320  * |   3  1 |   3  3 |  1  3
. . . . x |   2 |   * 80    0  4 |   0  6 |  0  4
----------+-----+--------+--------+--------+------
. . o3x . |   3 |   3  0 | 320  * |   2  1 |  1  2
. . . x4x |   8 |   4  4 |   * 80 |   0  3 |  0  3
----------+-----+--------+--------+--------+------
. o3o3x .    4 |   6  0 |   4  0 | 160  * |  1  1
. . o3x4x   24 |  24 12 |   8  6 |   * 40 |  0  2
----------+-----+--------+--------+--------+------
o3o3o3x .    5 |  10  0 |  10  0 |   5  0 | 32  *
. o3o3x4x   64 |  96 32 |  64 24 |  16  8 |  * 10

snubbed forms: o3o3o3x4s

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