Acronym squippyp, K-4.12
Name square-pyramidal prism,
J1 prism,
line || cube,
digonal magnabicupolaic ring
|,>,O device line prism pyramid prism = ||>|
Segmentochoron display  
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art
   x o   
         
         
x x   x x
Coordinates (1/sqrt(2), 0, 0, 1/2)   & all permutations in all but last coord., all changes of sign in all but first coord.
Dihedral angles
  • at {4} between trip and trip:   arccos(-1/3) = 109.471221°
  • at {4} between squippy and cube:   90°
  • at {3} between squippy and trip:   90°
  • at {4} between cube and trip:   arccos(1/sqrt(3)) = 54.735610°
Confer
related segmentochora:
n-pyp   {n} || 2n-p   ope  
related CRFs:
esquippidpy  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

xx ox4oo&#x   → height = 1/sqrt(2) = 0.707107
(line || cube)

o. o.4o.    | 2 * | 1 4 0 0 | 4 4 0 0 | 4 1 0
.o .o4.o    | * 8 | 0 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+---------+---------+------
x. .. ..    | 2 0 | 1 * * * | 4 0 0 0 | 4 0 0
oo oo4oo&#x | 1 1 | * 8 * * | 1 2 0 0 | 2 1 0
.x .. ..    | 0 2 | * * 4 * | 1 0 2 0 | 2 0 1
.. .x ..    | 0 2 | * * * 8 | 0 1 1 1 | 1 1 1
------------+-----+---------+---------+------
xx .. ..&#x | 2 2 | 1 2 1 0 | 4 * * * | 2 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 | * 8 * * | 1 1 0
.x .x ..    | 0 4 | 0 0 2 2 | * * 4 * | 1 0 1
.. .x4.o    | 0 4 | 0 0 0 4 | * * * 2 | 0 1 1
------------+-----+---------+---------+------
xx ox ..&#x  2 4 | 1 4 2 2 | 2 2 1 0 | 4 * *
.. ox4oo&#x  1 4 | 0 4 0 4 | 0 4 0 1 | * 2 *
.x .x4.o     0 8 | 0 0 4 8 | 0 0 4 2 | * * 1

{4} || trip   → height = sqrt(2/3) = 0.816497

  4 * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
  * 2 * | 0 0 2 0 1 2 0 0 | 0 2 1 0 0 2 2 1 0 | 1 0 2 1 1
  * * 4 | 0 0 0 1 0 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
--------+-----------------+-------------------+----------
  2 0 0 | 2 * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
  2 0 0 | * 2 * * * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
  1 1 0 | * * 4 * * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
  1 0 1 | * * * 4 * * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
  0 2 0 | * * * * 1 * * * | 0 2 0 0 0 0 2 0 0 | 1 0 2 0 1
  0 1 1 | * * * * * 4 * * | 0 0 0 0 0 1 1 1 0 | 0 0 1 1 1
  0 0 2 | * * * * * * 2 * | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1
  0 0 2 | * * * * * * * 2 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
--------+-----------------+-------------------+----------
  4 0 0 | 2 2 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
  2 2 0 | 1 0 2 0 1 0 0 0 | * 2 * * * * * * * | 1 0 1 0 0
  2 1 0 | 0 1 2 0 0 0 0 0 | * * 2 * * * * * * | 1 0 0 1 0
  2 0 2 | 1 0 0 2 0 0 1 0 | * * * 2 * * * * * | 0 1 1 0 0
  2 0 2 | 0 1 0 2 0 0 0 1 | * * * * 2 * * * * | 0 1 0 1 0
  1 1 1 | 0 0 1 1 0 1 0 0 | * * * * * 4 * * * | 0 0 1 1 0
  0 2 2 | 0 0 0 0 1 2 1 0 | * * * * * * 2 * * | 0 0 1 0 1
  0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * * * 2 * | 0 0 0 1 1
  0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * 1 | 0 1 0 0 1
--------+-----------------+-------------------+----------
 4 2 0 | 2 2 4 0 1 0 0 0 | 1 2 2 0 0 0 0 0 0 | 1 * * * *
 4 0 4 | 2 2 0 4 0 0 2 2 | 1 0 0 2 2 0 0 0 1 | * 1 * * *
 2 2 2 | 1 0 2 2 1 2 1 0 | 0 1 0 1 0 2 1 0 0 | * * 2 * *
 2 1 2 | 0 1 2 2 0 2 0 1 | 0 0 1 0 1 2 0 1 0 | * * * 2 *
 0 2 4 | 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 2 2 1 | * * * * 1

squippy || squippy   → height = 1

  1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0  top-tip
  * 4 * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0  top-base
  * * 1 * | 0 1 0 0 4 0 | 0 4 0 0 4 0 | 0 4 0 1  bottom-tip
  * * * 4 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1  bottom-base
----------+-------------+-------------+--------
  1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
  1 0 1 0 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0
  0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0
  0 1 0 1 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0
  0 0 1 1 | * * * * 4 * | 0 1 0 0 2 0 | 0 2 0 1
  0 0 0 2 | * * * * * 4 | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
  1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0
  1 1 1 1 | 1 1 0 1 1 0 | * 4 * * * * | 0 2 0 0
  0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0
  0 2 0 2 | 0 0 1 2 0 1 | * * * 4 * * | 0 1 1 0
  0 0 1 2 | 0 0 0 0 2 1 | * * * * 4 * | 0 1 0 1
  0 0 0 4 | 0 0 0 0 0 4 | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
 1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * *
 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 4 * *
 0 4 0 4 | 0 0 4 4 0 4 | 0 0 1 4 0 1 | * * 1 *
 0 0 1 4 | 0 0 0 0 4 4 | 0 0 0 0 4 1 | * * * 1

oxxo4oooo&#xr   → height(1,2) = height(3,4) = sqrt(1-[1/4 *sin^2(π/n)])
                  height(1,4) = height(2,3) = 1
( (pt || {4})  ||  (pt || {4}) )

o...4o...     | 1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0
.o..4.o..     | * 4 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
..o.4..o.     | * * 4 * | 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1
...o4...o     | * * * 1 | 0 1 0 0 0 4 | 0 4 0 0 0 4 | 0 4 0 1
--------------+---------+-------------+-------------+--------
oo..4oo..&#x  | 1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o..o4o..o&#x  | 1 0 0 1 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0
.x.. ....     | 0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0
.oo.4.oo.&#x  | 0 1 1 0 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0
..x. ....     | 0 0 2 0 | * * * * 4 * | 0 0 0 1 1 1 | 0 1 1 1
..oo4..oo&#x  | 0 0 1 1 | * * * * * 4 | 0 1 0 0 0 2 | 0 2 0 1
--------------+---------+-------------+-------------+--------
ox.. ....&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0
oooo4oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * 4 * * * * | 0 2 0 0
.x..4.o..     | 0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0
.xx. ....&#x  | 0 2 2 0 | 0 0 1 2 1 0 | * * * 4 * * | 0 1 1 0
..x.4..o.     | 0 0 4 0 | 0 0 0 0 4 0 | * * * * 1 * | 0 0 1 1
..xo ....&#x  | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * 4 | 0 1 0 1
--------------+---------+-------------+-------------+--------
ox..4oo..&#x   1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * *
oxxo ....&#xr  1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * 4 * *
.xx.4.oo.&#x   0 4 4 0 | 0 0 4 4 4 0 | 0 0 1 4 1 0 | * * 1 *
..xo4..oo&#x   0 0 4 1 | 0 0 0 0 4 4 | 0 0 0 0 1 4 | * * * 1

o(xo)x4o(oo)o&#xt 
(pt || ({4} || pt) || para {4})

o(..).4o(..).     | 1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0
.(o.).4.(o.).     | * 4 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.(.o).4.(.o).     | * * 1 * | 0 1 0 0 4 0 | 0 4 0 0 4 0 | 0 4 0 1
.(..)o4.(..)o     | * * * 4 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1
------------------+---------+-------------+-------------+--------
o(o.).4o(o.).&#x  | 1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o(.o).4o(.o).&#x  | 1 0 1 0 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0
.(x.). .(..).     | 0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0
.(o.)o4.(o.)o&#x  | 0 1 0 1 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0
.(.o)o4.(.o)o&#x  | 0 0 1 1 | * * * * 4 * | 0 1 0 0 2 0 | 0 2 0 1
.(..)x .(..).     | 0 0 0 2 | * * * * * 4 | 0 0 0 1 1 1 | 0 1 1 1
------------------+---------+-------------+-------------+--------
o(x.). .(..).&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0
o(oo)o4o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * 4 * * * * | 0 2 0 0
.(x.).4.(o.).     | 0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0
.(x.)x .(..).&#x  | 0 2 0 2 | 0 0 1 2 0 1 | * * * 4 * * | 0 1 1 0
.(.o)x .(..).&#x  | 0 0 1 2 | 0 0 0 0 2 1 | * * * * 4 * | 0 1 0 1
.(..)x4.(..)o     | 0 0 0 4 | 0 0 0 0 0 4 | * * * * * 1 | 0 0 1 1
------------------+---------+-------------+-------------+--------
o(x.).4o(o.).&#x   1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * *
o(xo)x .(..).&#xt  1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 4 * *
.(x.)x4.(o.)o&#x   0 4 0 4 | 0 0 4 4 0 4 | 0 0 1 4 0 1 | * * 1 *
.(.o)x4.(.o)o&#x   0 0 1 4 | 0 0 0 0 4 4 | 0 0 0 0 4 1 | * * * 1

© 2004-2018
top of page