Acronym tutcup (alt.: pabdirit, tutaltut), tut || inv tut, K-4.55
Name truncated tetrahedral cupoliprism,
runcic snub cubic hosochoron,
truncated tetrahedron atop inverted truncated tetrahedron,
truncated tetrahedron atop alternate truncated tetrahedron,
tetrahedrally medial part of rectified tesseract,
parabidiminished rectified tesseract
 
 ©
Segmentochoron display
Circumradius sqrt(3/2) = 1.224745
Lace city
in approx. ASCII-art
    x3x o3x
           
  u3o o3u  
           
x3o x3x    
Coordinates (3, 1, 1, 1)/sqrt(8)       all permutations in first 3 coords, even changes of sign in all coords
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
Confer
uniform relative:
rit  
segmentochora:
tet || tut  
related CRFs:
mibdirit  
general polytopal classes:
segmentochora   scaliform  
External
links
hedrondude   wikipedia   quickfur  

This polychoron also can be derived as equatorial stratos of rit, if that one will be considered with respect to an axial tetrahedral symmetry.

Klitzing in automn of 2000 both found this very polychoron and also obtained therefrom the precise concept of some weakening of uniformity, which shortly thereafter became known as scaliformity. Thus tutcup truely was the first known scaliform polytope!


Incidence matrix according to Dynkin symbol

xo3xx3ox&#x   → height = 1/sqrt(2) = 0.707107
(tut || inv tut)

o.3o.3o.    | 12  * | 1  2  2  0 0 | 2 1  2  2  1 0 0 | 1 2 1 1 0
.o3.o3.o    |  * 12 | 0  0  2  2 1 | 0 0  1  2  2 1 2 | 0 1 1 2 1
------------+-------+--------------+------------------+----------
x. .. ..    |  2  0 | 6  *  *  * * | 2 0  2  0  0 0 0 | 1 2 1 0 0
.. x. ..    |  2  0 | * 12  *  * * | 1 1  0  1  0 0 0 | 1 1 0 0 0
oo3oo3oo&#x |  1  1 | *  * 24  * * | 0 0  1  1  1 0 0 | 0 1 1 1 0
.. .x ..    |  0  2 | *  *  * 12 * | 0 0  0  1  0 1 1 | 0 1 0 1 1
.. .. .x    |  0  2 | *  *  *  * 6 | 0 0  0  0  2 0 2 | 0 0 1 2 1
------------+-------+--------------+------------------+----------
x.3x. ..&#x |  6  0 | 3  3  0  0 0 | 4 *  *  *  * * * | 1 1 0 0 0
.. x.3o.    |  3  0 | 0  3  0  0 0 | * 4  *  *  * * * | 1 0 0 1 0
xo .. ..&#x |  2  1 | 1  0  2  0 0 | * * 12  *  * * * | 0 1 1 0 0
.. xx ..&#x |  2  2 | 0  1  2  1 0 | * *  * 12  * * * | 0 1 0 1 0
.. .. ox&#x |  1  2 | 0  0  2  0 1 | * *  *  * 12 * * | 0 0 1 1 0
.o3.x ..    |  0  3 | 0  0  0  3 0 | * *  *  *  * 4 * | 0 1 0 0 1
.. .x3.x&#x |  0  6 | 0  0  0  3 3 | * *  *  *  * * 4 | 0 0 0 1 1
------------+-------+--------------+------------------+----------
x.3x.3o.     12  0 | 6 12  0  0 0 | 4 4  0  0  0 0 0 | 1 * * * *
xo3xx ..&#x   6  3 | 3  3  6  3 0 | 1 0  3  3  0 1 0 | * 4 * * *
xo .. ox&#x   2  2 | 1  0  4  0 1 | 0 0  2  0  2 0 0 | * * 6 * *
.. xx3ox&#x   3  6 | 0  3  6  3 3 | 0 1  0  3  3 0 1 | * * * 4 *
.o3.x3.x      0 12 | 0  0  0 12 6 | 0 0  0  0  0 4 4 | * * * * 1
or
o.3o.3o.    & | 24 |  1  2  2 | 2 1  3  2 | 1 3 1
--------------+----+----------+-----------+------
x. .. ..    & |  2 | 12  *  * | 0 0  2  0 | 1 2 1
.. x. ..    & |  2 |  * 24  * | 1 1  0  1 | 1 2 0
oo3oo3oo&#x   |  2 |  *  * 24 | 0 0  2  1 | 0 2 1
--------------+----+----------+-----------+------
x.3x. ..&#x & |  6 |  3  3  0 | 8 *  *  * | 1 1 0
.. x.3o.    & |  3 |  0  3  0 | * 8  *  * | 1 1 0
xo .. ..&#x & |  3 |  1  0  2 | * * 24  * | 0 1 1
.. xx ..&#x   |  4 |  0  2  2 | * *  * 12 | 0 2 0
--------------+----+----------+-----------+------
x.3x.3o.    &  12 |  6 12  0 | 4 4  0  0 | 2 * *
xo3xx ..&#x &   9 |  3  6  6 | 3 1  3  3 | * 8 *
xo .. ox&#x     4 |  2  0  4 | 0 0  4  0 | * * 6

s4o3x2s

demi( . . . . ) | 24 |  2  1  2 | 1  2 2  3 | 1 1 3
----------------+----+----------+-----------+------
demi( . . x . ) |  2 | 24  *  * | 1  1 1  0 | 1 0 2
      s4o . .   |  2 |  * 12  * | 0  0 2  2 | 1 1 2
      s . 2 s   |  2 |  *  * 24 | 0  1 0  2 | 0 1 2
----------------+----+----------+-----------+------
demi( . o3x . ) |  3 |  3  0  0 | 8  * *  * | 1 0 1
      s 2 x2s   |  4 |  2  0  2 | * 12 *  * | 0 0 2
sefa( s4o3x . ) |  6 |  3  3  0 | *  * 8  * | 1 0 1
sefa( s4o 2 s ) |  3 |  0  1  2 | *  * * 24 | 0 1 1
----------------+----+----------+-----------+------
      s4o3x .    12 | 12  6  0 | 4  0 4  0 | 2 * *
      s4o 2 s     4 |  0  2  4 | 0  0 0  4 | * 6 *
sefa( s4o3x2s )   9 |  6  3  6 | 1  3 1  3 | * * 8

starting figure: x4o3x x

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