| Acronym | tuta (alt.: pabdirit, tutcup, tutaltut), tut || inv tut, K-4.55 |
| Name | truncated tetrahedral alterprism, truncated tetrahedral cupoliprism, runcic snub cubic hosochoron, truncated tetrahedron atop invertedtruncated tetrahedron, truncated tetrahedron atop alternatetruncated tetrahedron, tetrahedrally medial part ofrectified tesseract, parabidiminishedrectified tesseract |
| Segmentochoron display / VRML |
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| Cross sections |
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| 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 | |
| Face vector | 24, 60, 52, 16 |
| Confer |
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| External links |     |
This polychoron also can be derived as equatorial stratos ofrit, if that one will be considered with respect to an axialtetrahedral 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 asscaliformity. Thus tutcup truely was the first known scaliform polytope!
Incidence matrix according toDynkin symbol
xo3xx3ox&#x → height = 1/sqrt(2) = 0.707107(tut|| invtut)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 0oo3oo3oo&#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 0xo .. ..&#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 | * * * *1oro.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 0oo3oo3oo&#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 0xo .. ..&#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
s4o3x2sdemi( . . . . ) | 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 2sefa( s4o3x . ) | 6 | 3 3 0 | * * 8 * | 1 0 1sefa( 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 | * * 8starting figure:x4o3x x
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