Acronym	tan
Name	truncated penteract
Field of sections	©
Circumradius	sqrt[13+8 sqrt(2)]/2 = 2.465447
Inradius wrt. pen	(5+4 sqrt(2))/sqrt(20) = 2.382945
Inradius wrt. tat	[1+sqrt(2)]/2 = 1.207107
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°
Face vector	160, 400, 400, 200, 42
Confer	general polytopal classes: Wythoffian polytera   analogs: truncated hypercube tCn
External links

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