Acronym tetaltut, tet || inv. tut
Name (degenerate) tetrahedron atop inverted truncated tetrahedron,
(degenerate) tetrahedron atop alternate truncated tetrahedron
 
 ©
Segmentochoron display
Circumradius ∞   i.e. flat in euclidean space
Dihedral angles
  • at {3} between hippy and oct:   180°
  • at {3} between hippy and tet (asym):   180°
  • at {3} between oct and tet (sym):   180°
  • at {3} between oct and tet (asym):   180°
  • at {6} between hippy and tut:   0°
  • at {3} between oct and tut:   0°
Confer
general polytopal classes:
segmentochora   lace simplices   decomposition  

It either can be thought of as a degenerate 4D segmentotope with zero height, or as a 3D euclidean decomposition of the larger base into smaller bits.


Incidence matrix according to Dynkin symbol

ox3ox3xo&#x   → height = 0
(tet || inv. tut)

o.3o.3o.    | 4  * | 3  6 0  0 | 3  3  3  6 0 0 | 1 1 3 3 0
.o3.o3.o    | * 12 | 0  2 1  2 | 0  2  2  1 2 1 | 0 2 1 1 1
------------+------+-----------+----------------+----------
.. .. x.    | 2  0 | 6  * *  * | 2  0  0  2 0 0 | 1 0 1 2 0
oo3oo3oo&#x | 1  1 | * 24 *  * | 0  1  1  1 0 0 | 0 1 1 1 0
.x .. ..    | 0  2 | *  * 6  * | 0  2  0  0 2 0 | 0 2 1 0 1
.. .x ..    | 0  2 | *  * * 12 | 0  0  1  0 1 1 | 0 1 0 1 1
------------+------+-----------+----------------+----------
.. o.3x.    | 3  0 | 3  0 0  0 | 4  *  *  * * * | 1 0 0 1 0
ox .. ..&#x | 1  2 | 0  2 1  0 | * 12  *  * * * | 0 1 1 0 0
.. ox ..&#x | 1  2 | 0  2 0  1 | *  * 12  * * * | 0 1 0 1 0
.. .. xo&#x | 2  1 | 1  2 0  0 | *  *  * 12 * * | 0 0 1 1 0
.x3.x ..    | 0  6 | 0  0 3  3 | *  *  *  * 4 * | 0 1 0 0 1
.. .x3.o    | 0  3 | 0  0 0  3 | *  *  *  * * 4 | 0 0 0 1 1
------------+------+-----------+----------------+----------
o.3o.3x.     4  0 | 6  0 0  0 | 4  0  0  0 0 0 | 1 * * * *
ox3ox ..&#x  1  6 | 0  6 3  3 | 0  3  3  0 1 0 | * 4 * * *
ox .. xo&#x  2  2 | 1  4 1  0 | 0  2  0  2 0 0 | * * 6 * *
.. ox3xo&#x  3  3 | 3  6 0  3 | 1  0  3  3 0 1 | * * * 4 *
.x3.x3.o     0 12 | 0  0 6 12 | 0  0  0  0 4 4 | * * * * 1

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