Acronym tuttip, K-4.57
Name truncated-tetrahedron prism
Segmentochoron display
Cross sections
 ©
Circumradius sqrt(13/8) = 1.274755
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {4} between hip and trip:   arccos(-1/3) = 109.471221°
  • at {6} between hip and tut:   90°
  • at {3} between trip and tut:   90°
  • at {4} between hip and hip:   arccos(1/3) = 70.528779°
Confer
general polytopal classes:
segmentochora   bistratic lace towers  
External
links
hedrondude  

Incidence matrix according to Dynkin symbol

x x3x3o

. . . . | 24 |  1  1  2 | 1  2 2 1 | 2 1 1
--------+----+----------+----------+------
x . . . |  2 | 12  *  * | 1  2 0 0 | 2 1 0
. x . . |  2 |  * 12  * | 1  0 2 0 | 2 0 1
. . x . |  2 |  *  * 24 | 0  1 1 1 | 1 1 1
--------+----+----------+----------+------
x x . . |  4 |  2  2  0 | 6  * * * | 2 0 0
x . x . |  4 |  2  0  2 | * 12 * * | 1 1 0
. x3x . |  6 |  0  3  3 | *  * 8 * | 1 0 1
. . x3o |  3 |  0  0  3 | *  * * 8 | 0 1 1
--------+----+----------+----------+------
x x3x .  12 |  6  6  6 | 3  3 2 0 | 4 * *
x . x3o   6 |  3  0  6 | 0  3 0 2 | * 4 *
. x3x3o  12 |  0  6 12 | 0  0 4 4 | * * 2

x x3x3/2o

. . .   . | 24 |  1  1  2 | 1  2 2 1 | 2 1 1
----------+----+----------+----------+------
x . .   . |  2 | 12  *  * | 1  2 0 0 | 2 1 0
. x .   . |  2 |  * 12  * | 1  0 2 0 | 2 0 1
. . x   . |  2 |  *  * 24 | 0  1 1 1 | 1 1 1
----------+----+----------+----------+------
x x .   . |  4 |  2  2  0 | 6  * * * | 2 0 0
x . x   . |  4 |  2  0  2 | * 12 * * | 1 1 0
. x3x   . |  6 |  0  3  3 | *  * 8 * | 1 0 1
. . x3/2o |  3 |  0  0  3 | *  * * 8 | 0 1 1
----------+----+----------+----------+------
x x3x   .  12 |  6  6  6 | 3  3 2 0 | 4 * *
x . x3/2o   6 |  3  0  6 | 0  3 0 2 | * 4 *
. x3x3/2o  12 |  0  6 12 | 0  0 4 4 | * * 2

x2x3o4s

demi( . . . . ) | 24 |  1  2  1 |  2 1 1 2 | 1 1 2
----------------+----+----------+----------+------
demi( x . . . ) |  2 | 12  *  * |  2 0 1 0 | 1 0 2
demi( . x . . ) |  2 |  * 24  * |  1 1 0 1 | 1 1 1
      . . o4s   |  2 |  *  * 12 |  0 0 1 2 | 0 1 2
----------------+----+----------+----------+------
demi( x x . . ) |  4 |  2  2  0 | 12 * * * | 1 0 1
demi( . x3o . ) |  3 |  0  3  0 |  * 8 * * | 1 1 0
      x 2 o4s   |  4 |  2  0  2 |  * * 6 * | 0 0 2
sefa( . x3o4s ) |  6 |  0  3  3 |  * * * 8 | 0 1 1
----------------+----+----------+----------+------
demi( x x3o . )   6 |  3  6  0 |  3 2 0 0 | 4 * *
      . x3o4s    12 |  0 12  6 |  0 4 0 4 | * 2 *
sefa( x2x3o4s )  12 |  6  6  6 |  3 0 3 2 | * * 4

starting figure: x x3o4x

xx3xx3oo&#x   → height = 1
(tut || tut)

o.3o.3o.    | 12  * | 1  2  1 0  0 | 2 1 1  2 0 0 | 1 2 1 0
.o3.o3.o    |  * 12 | 0  0  1 1  2 | 0 0 1  2 2 1 | 0 2 1 1
------------+-------+--------------+--------------+--------
x. .. ..    |  2  0 | 6  *  * *  * | 2 0 1  0 0 0 | 1 2 0 0
.. x. ..    |  2  0 | * 12  * *  * | 1 1 0  1 0 0 | 1 1 1 0
oo3oo3oo&#x |  1  1 | *  * 12 *  * | 0 0 1  2 0 0 | 0 2 1 0
.x .. ..    |  0  2 | *  *  * 6  * | 0 0 1  0 2 0 | 0 2 0 1
.. .x ..    |  0  2 | *  *  * * 12 | 0 0 0  1 1 1 | 0 1 1 1
------------+-------+--------------+--------------+--------
x.3x. ..    |  6  0 | 3  3  0 0  0 | 4 * *  * * * | 1 1 0 0
.. x.3o.    |  3  0 | 0  3  0 0  0 | * 4 *  * * * | 1 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * 6  * * * | 0 2 0 0
.. xx ..&#x |  2  2 | 0  1  2 0  1 | * * * 12 * * | 0 1 1 0
.x3.x ..    |  0  6 | 0  0  0 3  3 | * * *  * 4 * | 0 1 0 1
.. .x3.o    |  0  3 | 0  0  0 0  3 | * * *  * * 4 | 0 0 1 1
------------+-------+--------------+--------------+--------
x.3x.3o.     12  0 | 6 12  0 0  0 | 4 4 0  0 0 0 | 1 * * *
xx3xx ..&#x   6  6 | 3  3  6 3  3 | 1 0 3  3 1 0 | * 4 * *
.. xx3oo&#x   3  3 | 0  3  3 0  3 | 0 1 0  3 0 1 | * * 4 *
.x3.x3.o      0 12 | 0  0  0 6 12 | 0 0 0  0 4 4 | * * * 1

xxx xux3oox&#xt   → both heights = sqrt(2/3) = 0.816497
(trip || pseudo (u,x)-trip || hip)

o.. o..3o..     | 6 *  * | 1 2 1 0  0 0 0 0 | 2 1 1 2 0 0 0 0 0 | 1 2 1 0 0
.o. .o.3.o.     | * 6  * | 0 0 1 1  2 0 0 0 | 0 0 1 2 2 1 0 0 0 | 0 2 1 1 0
..o ..o3..o     | * * 12 | 0 0 0 0  1 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
----------------+--------+------------------+-------------------+----------
x.. ... ...     | 2 0  0 | 3 * * *  * * * * | 2 0 1 0 0 0 0 0 0 | 1 2 0 0 0
... x.. ...     | 2 0  0 | * 6 * *  * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo. oo.3oo.&#x  | 1 1  0 | * * 6 *  * * * * | 0 0 1 2 0 0 0 0 0 | 0 2 1 0 0
.x. ... ...     | 0 2  0 | * * * 3  * * * * | 0 0 1 0 2 0 0 0 0 | 0 2 0 1 0
.oo .oo3.oo&#x  | 0 1  1 | * * * * 12 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
..x ... ...     | 0 0  2 | * * * *  * 6 * * | 0 0 0 0 1 0 1 1 0 | 0 1 0 1 1
... ..x ...     | 0 0  2 | * * * *  * * 6 * | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1
... ... ..x     | 0 0  2 | * * * *  * * * 6 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
----------------+--------+------------------+-------------------+----------
x.. x.. ...     | 4 0  0 | 2 2 0 0  0 0 0 0 | 3 * * * * * * * * | 1 1 0 0 0
... x..3o..     | 3 0  0 | 0 3 0 0  0 0 0 0 | * 2 * * * * * * * | 1 0 1 0 0
xx. ... ...&#x  | 2 2  0 | 1 0 2 1  0 0 0 0 | * * 3 * * * * * * | 0 2 0 0 0
... xux ...&#xt | 2 2  2 | 0 1 2 0  2 0 1 0 | * * * 6 * * * * * | 0 1 1 0 0
.xx ... ...&#x  | 0 2  2 | 0 0 0 1  2 1 0 0 | * * * * 6 * * * * | 0 1 0 1 0
... ... .ox&#x  | 0 1  2 | 0 0 0 0  2 0 0 1 | * * * * * 6 * * * | 0 0 1 1 0
..x ..x ...     | 0 0  4 | 0 0 0 0  0 2 2 0 | * * * * * * 3 * * | 0 1 0 0 1
..x ... ..x     | 0 0  4 | 0 0 0 0  0 2 0 2 | * * * * * * * 3 * | 0 0 0 1 1
... ..x3..x     | 0 0  6 | 0 0 0 0  0 0 3 3 | * * * * * * * * 2 | 0 0 1 0 1
----------------+--------+------------------+-------------------+----------
x.. x..3o..      6 0  0 | 3 6 0 0  0 0 0 0 | 3 2 0 0 0 0 0 0 0 | 1 * * * *
xxx xux ...&#xt  4 4  4 | 2 2 4 2  4 2 2 0 | 1 0 2 2 2 0 1 0 0 | * 3 * * *
... xux3oox&#xt  3 3  6 | 0 3 3 0  6 0 3 3 | 0 1 0 3 0 3 0 0 1 | * * 2 * *
.xx ... .ox&#x   0 2  4 | 0 0 0 1  4 2 0 2 | 0 0 0 0 2 2 0 1 0 | * * * 3 *
..x ..x3..x      0 0 12 | 0 0 0 0  0 6 6 6 | 0 0 0 0 0 0 3 3 2 | * * * * 1

x(xu)(xu)x-3-x(xo)(oo)o-&#xr   cycle (abefdc)
                               height(a,b) = height(c,e) = height(d,f) = 1
                               height(a,c) = height(b,e) = height(c,d) = height(e,f) = sqrt(2/3) = 0.816497

o(..)(..).-3-o(..)(..).      | 6 * * * * * | 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 0 | 1 1 1 1 0 0
.(o.)(..).-3-.(o.)(..).      | * 6 * * * * | 0 0 1 0 1 1 1 0 0 0 0 0 0 | 0 1 1 0 0 1 1 1 1 0 0 0 0 | 1 1 1 0 1 0
.(.o)(..).-3-.(.o)(..).      | * * 3 * * * | 0 0 0 2 0 0 0 1 1 0 0 0 0 | 0 0 0 2 1 2 0 0 0 1 0 0 0 | 0 2 1 1 0 0
.(..)(o.).-3-.(..)(o.).      | * * * 3 * * | 0 0 0 0 0 0 0 1 0 2 1 0 0 | 0 0 0 2 0 0 0 0 0 1 1 2 0 | 0 2 0 1 0 1
.(..)(.o).-3-.(..)(.o).      | * * * * 3 * | 0 0 0 0 0 0 2 0 1 0 0 1 0 | 0 0 0 0 0 2 0 2 1 1 0 0 0 | 0 2 1 0 1 0
.(..)(..)o-3-.(..)(..)o      | * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 1 1 2 | 0 0 0 0 0 0 0 2 0 1 0 2 1 | 0 2 0 0 1 1
-----------------------------+-------------+---------------------------+---------------------------+------------
x(..)(..).   .(..)(..).      | 2 0 0 0 0 0 | 3 * * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
.(..)(..).   x(..)(..).      | 2 0 0 0 0 0 | * 3 * * * * * * * * * * * | 1 0 1 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
o(o.)(..).-3-o(o.)(..).-&#x  | 1 1 0 0 0 0 | * * 6 * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0
o(.o)(..).-3-o(.o)(..).-&#x  | 1 0 1 0 0 0 | * * * 6 * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
.(x.)(..).   .(..)(..).      | 0 2 0 0 0 0 | * * * * 3 * * * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 0 0 | 1 1 0 0 1 0
.(..)(..).   .(x.)(..).      | 0 2 0 0 0 0 | * * * * * 3 * * * * * * * | 0 0 1 0 0 0 1 0 1 0 0 0 0 | 1 0 1 0 1 0
.(o.)(.o).-3-.(o.)(.o).-&#x  | 0 1 0 0 1 0 | * * * * * * 6 * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 0 1 0
.(.o)(o.).-3-.(.o)(o.).-&#x  | 0 0 1 1 0 0 | * * * * * * * 3 * * * * * | 0 0 0 2 0 0 0 0 0 1 0 0 0 | 0 2 0 1 0 0
.(.o)(.o).-3-.(.o)(.o).-&#x  | 0 0 1 0 1 0 | * * * * * * * * 3 * * * * | 0 0 0 0 0 2 0 0 0 1 0 0 0 | 0 2 1 0 0 0
.(..)(x.).   .(..)(..).      | 0 0 0 2 0 0 | * * * * * * * * * 3 * * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 1 0 1 0 1
.(..)(o.)o-3-.(..)(o.)o-&#x  | 0 0 0 1 0 1 | * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 0 0 1 0 2 0 | 0 2 0 0 0 1
.(..)(.o)o-3-.(..)(.o)o-&#x  | 0 0 0 0 1 1 | * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 2 0 1 0 0 0 | 0 2 0 0 1 0
.(..)(..)x   .(..)(..).      | 0 0 0 0 0 2 | * * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 1 0 0 1 1
-----------------------------+-------------+---------------------------+---------------------------+------------
x(..)(..).-3-x(..)(..).      | 6 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * | 1 0 0 1 0 0
x(x.)(..).   .(..)(..).-&#x  | 2 2 0 0 0 0 | 1 0 2 0 1 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * | 1 1 0 0 0 0
.(..)(..).   x(x.)(..).-&#x  | 2 2 0 0 0 0 | 0 1 2 0 0 1 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * | 1 0 1 0 0 0
x(.u)(x.).   .(..)(..).-&#xt | 2 0 2 2 0 0 | 1 0 0 2 0 0 0 2 0 1 0 0 0 | * * * 3 * * * * * * * * * | 0 1 0 1 0 0
.(..)(..).   x(.o)(..).-&#x  | 2 0 1 0 0 0 | 0 1 0 2 0 0 0 0 0 0 0 0 0 | * * * * 3 * * * * * * * * | 0 0 1 1 0 0
o(oo)(.o).-3-o(oo)(.o).-&#xr | 1 1 1 0 1 0 | 0 0 1 1 0 0 1 0 1 0 0 0 0 | * * * * * 6 * * * * * * * | 0 1 1 0 0 0
.(x.)(..).-3-.(x.)(..).      | 0 6 0 0 0 0 | 0 0 0 0 3 3 0 0 0 0 0 0 0 | * * * * * * 1 * * * * * * | 1 0 0 0 1 0
.(x.)(.u)x   .(..)(..).-&#xt | 0 2 0 0 2 2 | 0 0 0 0 1 0 2 0 0 0 0 2 1 | * * * * * * * 3 * * * * * | 0 1 0 0 1 0
.(..)(..).   .(x.)(.o).-&#x  | 0 2 0 0 1 0 | 0 0 0 0 0 1 2 0 0 0 0 0 0 | * * * * * * * * 3 * * * * | 0 0 1 0 1 0
.(.o)(oo)o-3-.(.o)(oo)o-&#xr | 0 0 1 1 1 1 | 0 0 0 0 0 0 0 1 1 0 1 1 0 | * * * * * * * * * 3 * * * | 0 2 0 0 0 0
.(..)(x.).-3-.(..)(o.).      | 0 0 0 3 0 0 | 0 0 0 0 0 0 0 0 0 3 0 0 0 | * * * * * * * * * * 1 * * | 0 0 0 1 0 1
.(..)(x.)x   .(..)(..).-&#x  | 0 0 0 2 0 2 | 0 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * 3 * | 0 1 0 0 0 1
.(..)(..)x-3-.(..)(..)o      | 0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-----------------------------+-------------+---------------------------+---------------------------+------------
x(x.)(..).-3-x(x.)(..).-&#x   6 6 0 0 0 0 | 3 3 6 0 3 3 0 0 0 0 0 0 0 | 1 3 3 0 0 0 1 0 0 0 0 0 0 | 1 * * * * *
x(xu)(xu)x   .(..)(..).-&#xr  2 2 2 2 2 2 | 1 0 2 2 1 0 2 2 2 1 2 2 1 | 0 1 0 1 0 2 0 1 0 2 0 1 0 | * 3 * * * * cycle (abefdc)
.(..)(..).   x(xo)(.o).-&#xr  2 2 1 0 1 0 | 0 1 2 2 0 1 2 0 1 0 0 0 0 | 0 0 1 0 1 2 0 0 1 0 0 0 0 | * * 3 * * * cycle (abec)
x(.u)(x.).-3-x(.o)(o.).-&#xt  6 0 3 3 0 0 | 3 3 0 6 0 0 0 3 0 3 0 0 0 | 1 0 0 3 3 0 0 0 0 0 1 0 0 | * * * 1 * *
.(x.)(.u)x-3-.(x.)(.o)o-&#xt  0 6 0 0 3 3 | 0 0 0 0 3 3 6 0 0 0 0 3 3 | 0 0 0 0 0 0 1 3 3 0 0 0 1 | * * * * 1 *
.(..)(x.)x-3-.(..)(o.)o-&#x   0 0 0 3 0 3 | 0 0 0 0 0 0 0 0 0 3 3 0 3 | 0 0 0 0 0 0 0 0 0 0 1 3 1 | * * * * * 1

(even so a cycle of (D-2)-dimensional elements these are given here as axially stack of "layers",
 parantheses therefore refer to same axially heights of mutually shifted elements)

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