Acronym trippy, K-4.7
Name trigonal-prismatic pyramid,
vertex pyramid of the rectified pentachoron
|,>,O device line pyramid prism pyramid = |>|>
Segmentochoron display
Circumradius sqrt(3/5) = 0.774597
Lace city
in approx. ASCII-art 
   o3o   
         
x3o   x3o

  x o    
         
         
o o   x x
Volume sqrt(5)/32 = 0.069877
Dihedral angles
  • at {3} between squippy and tet:   arccos(-1/4) = 104.477512°
  • at {3} between squippy and squippy:   arccos(1/4) = 75.522488°
  • at {4} between squippy and trip:   arccos(sqrt[1/6]) = 65.905157°
  • at {3} between tet and trip:   arccos(sqrt[3/8]) = 52.238756°
Face vector 7, 15, 14, 6
Confer
general pyramids:
pt || n-p  
uniform relative:
rap  
related CRFs:
tript  
general polytopal classes:
segmentochora   lace simplices  
External
links 		polytopewiki  

Incidence matrix according to Dynkin symbol

ox ox3oo&#x   → height = sqrt(5/12) = 0.645497
(pt || trip)

o. o.3o.    | 1 * ♦ 6 0 0 | 3 6 0 0 | 3 2 0
.o .o3.o    | * 6 | 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+-------+---------+------
oo oo3oo&#x | 1 1 | 6 * * | 1 2 0 0 | 2 1 0
.x .. ..    | 0 2 | * 3 * | 1 0 2 0 | 2 0 1
.. .x ..    | 0 2 | * * 6 | 0 1 1 1 | 1 1 1
------------+-----+-------+---------+------
ox .. ..&#x | 1 2 | 2 1 0 | 3 * * * | 2 0 0
.. ox ..&#x | 1 2 | 2 0 1 | * 6 * * | 1 1 0
.x .x ..    | 0 4 | 0 2 2 | * * 3 * | 1 0 1
.. .x3.o    | 0 3 | 0 0 3 | * * * 2 | 0 1 1
------------+-----+-------+---------+------
ox ox ..&#x ♦ 1 4 | 4 2 2 | 2 2 1 0 | 3 * *
.. ox3oo&#x ♦ 1 3 | 3 0 3 | 0 3 0 1 | * 2 *
.x .x3.o    ♦ 0 6 | 0 3 6 | 0 0 3 2 | * * 1


xox3ooo&#x   → height(1,2) = height(2,3) = sqrt(2/3) = 0.816497
               height(1,3) = 1
               height(1,23) = sqrt(5/8) = 0.790569
               shear(1,23) = 1/sqrt(6) = 0.408248
({3} || tet)

o..3o..    | 3 * * | 2 1 1 0 0 | 1 2 2 1 0 0 | 1 1 2 0
.o.3.o.    | * 1 * ♦ 0 3 0 3 0 | 0 3 0 3 3 0 | 1 0 3 1
..o3..o    | * * 3 | 0 0 1 1 2 | 0 0 2 1 2 1 | 0 1 2 1
-----------+-------+-----------+-------------+--------
x.. ...    | 2 0 0 | 3 * * * * | 1 1 1 0 0 0 | 1 1 1 0
oo.3oo.&#x | 1 1 0 | * 3 * * * | 0 2 0 1 0 0 | 1 0 2 0
o.o3o.o&#x | 1 0 1 | * * 3 * * | 0 0 2 1 0 0 | 0 1 2 0
.oo3.oo&#x | 0 1 1 | * * * 3 * | 0 0 0 1 2 0 | 0 0 2 1
..x ...    | 0 0 2 | * * * * 3 | 0 0 1 0 1 1 | 0 1 1 1
-----------+-------+-----------+-------------+--------
x..3o..    | 3 0 0 | 3 0 0 0 0 | 1 * * * * * | 1 1 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 | * 3 * * * * | 1 0 1 0
x.x ...&#x | 2 0 2 | 1 0 2 0 1 | * * 3 * * * | 0 1 1 0
ooo3ooo&#x | 1 1 1 | 0 1 1 1 0 | * * * 3 * * | 0 0 2 0
.ox ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * 3 * | 0 0 1 1
..x3..o    | 0 0 3 | 0 0 0 0 3 | * * * * * 1 | 0 1 0 1
-----------+-------+-----------+-------------+--------
xo.3oo.&#x ♦ 3 1 0 | 3 3 0 0 0 | 1 3 0 0 0 0 | 1 * * *
x.x3o.o&#x ♦ 3 0 3 | 3 0 3 0 3 | 1 0 3 0 0 1 | * 1 * *
xox ...&#x ♦ 2 1 2 | 1 2 2 2 1 | 0 1 1 2 1 0 | * * 3 *
.ox3.oo&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 3 1 | * * * 1


line || squippy   → height = sqrt(5/8) = 0.790569
                   shear = 1/sqrt(8) = 0.353553

  2 * * | 1 1 2 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
  * 1 * ♦ 0 2 0 4 0 0 | 1 0 4 0 2 2 0 | 2 0 2 1
  * * 4 | 0 0 1 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
--------+-------------+---------------+--------
  2 0 0 | 1 * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
  1 1 0 | * 2 * * * * | 1 0 2 0 0 0 0 | 2 0 1 0
  1 0 1 | * * 4 * * * | 0 1 1 1 0 0 0 | 1 1 1 0
  0 1 1 | * * * 4 * * | 0 0 1 0 1 1 0 | 1 0 1 1
  0 0 2 | * * * * 2 * | 0 1 0 0 1 0 1 | 1 1 0 1 para
  0 0 2 | * * * * * 2 | 0 0 0 1 0 1 1 | 0 1 1 1 ortho
--------+-------------+---------------+--------
  2 1 0 | 1 2 0 0 0 0 | 1 * * * * * * | 2 0 0 0
  2 0 2 | 1 0 2 0 1 0 | * 2 * * * * * | 1 1 0 0
  1 1 1 | 0 1 1 1 0 0 | * * 4 * * * * | 1 0 1 0
  1 0 2 | 0 0 2 0 0 1 | * * * 2 * * * | 0 1 1 0
  0 1 2 | 0 0 0 2 1 0 | * * * * 2 * * | 1 0 0 1
  0 1 2 | 0 0 0 2 0 1 | * * * * * 2 * | 0 0 1 1
  0 0 4 | 0 0 0 0 2 2 | * * * * * * 1 | 0 1 0 1
--------+-------------+---------------+--------
♦ 2 1 2 | 1 2 2 2 1 0 | 1 1 2 0 1 0 0 | 2 * * *
♦ 2 0 4 | 1 0 4 0 2 2 | 0 2 0 2 0 0 1 | * 1 * *
♦ 1 1 2 | 0 1 2 2 0 1 | 0 0 2 1 0 1 0 | * * 2 *
♦ 0 1 4 | 0 0 0 4 2 2 | 0 0 0 0 2 2 1 | * * * 1


xoo xox&#x   → height(1,2) = 1/sqrt(2) = 0.707107
               height(1,3) = height(2,3) = sqrt(3)/2 = 0.866025

o.. o..    | 4 * * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1
.o. .o.    | * 1 * ♦ 0 0 4 0 2 0 | 0 2 2 0 0 4 1 | 1 0 2 2
..o ..o    | * * 2 | 0 0 0 2 1 1 | 0 0 0 1 2 2 1 | 0 1 1 2
-----------+-------+-------------+---------------+--------
x.. ...    | 2 0 0 | 2 * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
... x..    | 2 0 0 | * 2 * * * * | 1 0 1 0 1 0 0 | 1 1 0 1
oo. oo.&#x | 1 1 0 | * * 4 * * * | 0 1 1 0 0 1 0 | 1 0 1 1
o.o o.o&#x | 1 0 1 | * * * 4 * * | 0 0 0 1 1 1 0 | 0 1 1 1
.oo .oo&#x | 0 1 1 | * * * * 2 * | 0 0 0 0 0 2 1 | 0 0 1 2
... ..x    | 0 0 2 | * * * * * 1 | 0 0 0 0 2 0 1 | 0 1 0 2
-----------+-------+-------------+---------------+--------
x.. x..    | 4 0 0 | 2 2 0 0 0 0 | 1 * * * * * * | 1 1 0 0
xo. ...&#x | 2 1 0 | 1 0 2 0 0 0 | * 2 * * * * * | 1 0 1 0
... xo.&#x | 2 1 0 | 0 1 2 0 0 0 | * * 2 * * * * | 1 0 0 1
x.o ...&#x | 2 0 1 | 1 0 0 2 0 0 | * * * 2 * * * | 0 1 1 0
... x.x&#x | 2 0 2 | 0 1 0 2 0 1 | * * * * 2 * * | 0 1 0 1
ooo ooo&#x | 1 1 1 | 0 0 1 1 1 0 | * * * * * 4 * | 0 0 1 1
... .ox&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * 1 | 0 0 0 2
-----------+-------+-------------+---------------+--------
xo. xo.&#x ♦ 4 1 0 | 2 2 4 0 0 0 | 1 2 2 0 0 0 0 | 1 * * *
x.o x.x&#x ♦ 4 0 2 | 2 2 0 4 0 1 | 1 0 0 2 2 0 0 | * 1 * *
xoo ...&#x ♦ 2 1 1 | 1 0 2 2 1 0 | 0 1 0 1 0 2 0 | * * 2 *
... xox&#x ♦ 2 1 2 | 0 1 2 2 2 1 | 0 0 1 0 1 2 1 | * * * 2


oxxx&#x   → height(1,2) = height(1,3) = height(1,4) = sqrt(3)/2 = 0.866025
            height(2,3) = height(2,4) = height(3,4) = 1

o...    | 11 * * * ♦ 2 2 2 0 0 0 0 0 0 | 1 2 2 1 2 1 0 0 0 0 | 1 2 1 1 0
.o..    | * 2 * * | 1 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1
..o.    | * * 2 * | 0 1 0 0 1 0 1 1 0 | 0 1 0 1 1 0 1 1 0 1 | 1 1 0 1 1
...o    | * * * 2 | 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
--------+---------+-------------------+---------------------+----------
oo..&#x | 1 1 0 0 | 2 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
o.o.&#x | 1 0 1 0 | * 2 * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 1 1 0 1 0
o..o&#x | 1 0 0 1 | * * 2 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
.x..    | 0 2 0 0 | * * * 1 * * * * * | 1 0 0 0 0 0 1 0 1 0 | 1 0 1 0 1
.oo.&#x | 0 1 1 0 | * * * * 2 * * * * | 0 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1
.o.o&#x | 0 1 0 1 | * * * * * 2 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
..x.    | 0 0 2 0 | * * * * * * 1 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
..oo&#x | 0 0 1 1 | * * * * * * * 2 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
...x    | 0 0 0 2 | * * * * * * * * 1 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
--------+---------+-------------------+---------------------+----------
ox..&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 0 | 1 * * * * * * * * * | 1 0 1 0 0
ooo.&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | * 2 * * * * * * * * | 1 1 0 0 0
oo.o&#x | 1 1 0 1 | 1 0 1 0 0 1 0 0 0 | * * 2 * * * * * * * | 0 1 1 0 0
o.x.&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 0 | * * * 1 * * * * * * | 1 0 0 1 0
o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 | * * * * 2 * * * * * | 0 1 0 1 0
o..x&#x | 1 0 0 2 | 0 0 2 0 0 0 0 0 1 | * * * * * 1 * * * * | 0 0 1 1 0
.xx.&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 | * * * * * * * 2 * * | 0 1 0 0 1
.x.x&#x | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 | * * * * * * * * 1 * | 0 0 1 0 1
..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 | * * * * * * * * * 1 | 0 0 0 1 1
--------+---------+-------------------+---------------------+----------
oxx.&#x ♦ 1 2 2 0 | 2 2 0 1 2 0 1 0 0 | 1 2 0 1 0 0 1 0 0 0 | 1 * * * *
oooo&#x ♦ 1 1 1 1 | 1 1 1 0 1 1 0 1 0 | 0 1 1 0 1 0 0 1 0 0 | * 2 * * *
ox.x&#x ♦ 1 2 0 2 | 2 0 2 1 0 2 0 0 1 | 1 0 2 0 0 1 0 0 1 0 | * * 1 * *
o.xx&#x ♦ 1 0 2 2 | 0 2 2 0 0 0 1 2 1 | 0 0 0 1 2 1 0 0 0 1 | * * * 1 *
.xxx&#x ♦ 0 2 2 2 | 0 0 0 1 2 2 1 2 1 | 0 0 0 0 0 0 1 2 1 1 | * * * * 1

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