Acronym tan
Name truncated penteract
Field of sections
` ©`
wrt. pen
(5+4 sqrt(2))/sqrt(20) = 2.382945
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°
Confer
analogs:
truncated hypercube tCn
External

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
```