Acronym paw, K-4.133, {10} || pap
Name antipentawedge,
decagon - pentagonn-antiprismatic wedge,
pentagonal gyrobicupolaic ring,
{10} || pap,
{5} || gyrated pecu
Segmentochoron display
Circumradius sqrt[5+2 sqrt(5)] = 3.077684
Lace city
in approx. ASCII-art 
        x5x        
                   
x5o             o5x
Face vector 20, 50, 43, 13
Confer
related segmentochora:
idasrid  
segmentochora family:
{2n} || n-ap  
general polytopal classes:
segmentochora  
External
links 		polytopewiki

Incidence matrix according to Dynkin symbol

xxo5oxx&#x   → height(1,2) = height(2,3) = sqrt((5-sqrt(5))/10) = 0.525731
               height(1,3) = sqrt[(5+sqrt(5))/10] = 0.850651

o..5o..    | 5  * * | 2  2  2 0 0  0 0 | 1 2 1 2 1  2 0 0 0 0 | 1 1 2 1 0
.o.5.o.    | * 10 * | 0  1  0 1 1  1 0 | 0 1 1 0 0  1 1 1 1 0 | 1 0 1 1 1
..o5..o    | *  * 5 | 0  0  2 0 0  2 2 | 0 0 0 1 2  2 0 1 2 1 | 0 1 1 2 1
-----------+--------+------------------+----------------------+----------
x.. ...    | 2  0 0 | 5  *  * * *  * * | 1 1 0 1 0  0 0 0 0 0 | 1 1 1 0 0
oo.5oo.&#x | 1  1 0 | * 10  * * *  * * | 0 1 1 0 0  1 0 0 0 0 | 1 0 1 1 0
o.o5o.o&#x | 1  0 1 | *  * 10 * *  * * | 0 0 0 1 1  1 0 0 0 0 | 0 1 1 1 0
.x. ...    | 0  2 0 | *  *  * 5 *  * * | 0 1 0 0 0  0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0  2 0 | *  *  * * 5  * * | 0 0 1 0 0  0 1 0 1 0 | 1 0 0 1 1
.oo5.oo&#x | 0  1 1 | *  *  * * * 10 * | 0 0 0 0 0  1 0 1 1 0 | 0 0 1 1 1
... ..x    | 0  0 2 | *  *  * * *  * 5 | 0 0 0 0 1  0 0 0 1 1 | 0 1 0 1 1
-----------+--------+------------------+----------------------+----------
x..5o..    | 5  0 0 | 5  0  0 0 0  0 0 | 1 * * * *  * * * * * | 1 1 0 0 0
xx. ...&#x | 2  2 0 | 1  2  0 1 0  0 0 | * 5 * * *  * * * * * | 1 0 1 0 0
... ox.&#x | 1  2 0 | 0  2  0 0 1  0 0 | * * 5 * *  * * * * * | 1 0 0 1 0
x.o ...&#x | 2  0 1 | 1  0  2 0 0  0 0 | * * * 5 *  * * * * * | 0 1 1 0 0
... o.x&#x | 1  0 2 | 0  0  2 0 0  0 1 | * * * * 5  * * * * * | 0 1 0 1 0
ooo5ooo&#x | 1  1 1 | 0  1  1 0 0  1 0 | * * * * * 10 * * * * | 0 0 1 1 0
.x.5.x.    | 0 10 0 | 0  0  0 5 5  0 0 | * * * * *  * 1 * * * | 1 0 0 0 1
.xo ...&#x | 0  2 1 | 0  0  0 1 0  2 0 | * * * * *  * * 5 * * | 0 0 1 0 1
... .xx&#x | 0  2 2 | 0  0  0 0 1  2 1 | * * * * *  * * * 5 * | 0 0 0 1 1
..o5..x    | 0  0 5 | 0  0  0 0 0  0 5 | * * * * *  * * * * 1 | 0 1 0 0 1
-----------+--------+------------------+----------------------+----------
xx.5ox.&#x ♦ 5 10 0 | 5 10  0 5 5  0 0 | 1 5 5 0 0  0 1 0 0 0 | 1 * * * *
x.o5o.x&#x ♦ 5  0 5 | 5  0 10 0 0  0 5 | 1 0 0 5 5  0 0 0 0 1 | * 1 * * *
xxo ...&#x ♦ 2  2 1 | 1  2  2 1 0  2 0 | 0 1 0 1 0  2 0 1 0 0 | * * 5 * *
... oxx&#x ♦ 1  2 2 | 0  2  2 0 1  2 1 | 0 0 1 0 1  2 0 0 1 0 | * * * 5 *
.xo5.xx&#x ♦ 0 10 5 | 0  0  0 5 5 10 5 | 0 0 0 0 0  0 1 5 5 1 | * * * * 1


os2xo10os&#x   → height = (sqrt(5)-1)/4 = 0.309017
({10} || pap)

      o.2o.10o.      | 10  * |  2  2  0  0 | 1  1  2 0  2  0 | 2 0  2
demi( .o2.o10.o    ) |  * 10 |  0  2  2  2 | 0  2  1 1  2  3 | 1 1  3
---------------------+-------+-------------+-----------------+-------
      .. x.  ..      |  2  0 | 10  *  *  * | 1  0  1 0  1  0 | 2 0  1
demi( oo2oo10oo&#x ) |  1  1 |  * 20  *  * | 0  1  1 0  1  0 | 1 0  2
      .s .2  .s      |  0  2 |  *  * 10  * | 0  1  0 0  0  2 | 0 1  2
sefa( .. .o10.s    ) |  0  2 |  *  *  * 10 | 0  0  0 1  1  1 | 1 1  1
---------------------+-------+-------------+-----------------+-------
      .. x.10o.      | 10  0 | 10  0  0  0 | 1  *  * *  *  * | 2 0  0
      os .2  os&#x   |  1  2 |  0  2  1  0 | * 10  * *  *  * | 0 0  2
demi( .. xo  ..&#x ) |  2  1 |  1  2  0  0 | *  * 10 *  *  * | 1 0  1
      .. .o10.s      |  0  5 |  0  0  0  5 | *  *  * 2  *  * | 1 1  0
sefa( .. xo10os&#x ) |  2  2 |  1  2  0  1 | *  *  * * 10  * | 1 0  1
sefa( .s2.o10.s    ) |  0  3 |  0  0  2  1 | *  *  * *  * 10 | 0 1  1
---------------------+-------+-------------+-----------------+-------
      .. xo10os&#x   ♦ 10  5 | 10 10  0  5 | 1  0  5 1  5  0 | 2 *  *
      .s2.o10.s      ♦  0 10 |  0  0 10 10 | 0  0  0 2  0 10 | * 1  *
sefa( os2xo10os&#x ) ♦  2  3 |  1  4  2  1 | 0  2  1 0  1  1 | * * 10

starting figure: ox xo10ox&#x


{5} || gyro pecu   → height = 1/2

  5 *  * | 2  2  2 0  0 0 0 | 1 2 2 1  2 1 0 0 0 0 | 1 1 2 1 0
  * 5  * | 0  2  0 2  2 0 0 | 0 1 0 2  2 0 1 2 1 0 | 1 0 1 2 1
  * * 10 | 0  0  1 0  1 1 1 | 0 0 1 0  1 1 0 1 1 1 | 0 1 1 1 1
---------+------------------+----------------------+----------
  2 0  0 | 5  *  * *  * * * | 1 1 1 0  0 0 0 0 0 0 | 1 1 1 0 0
  1 1  0 | * 10  * *  * * * | 0 1 0 1  1 0 0 0 0 0 | 1 0 1 1 0
  1 0  1 | *  * 10 *  * * * | 0 0 1 0  1 1 0 0 0 0 | 0 1 1 1 0
  0 2  0 | *  *  * 5  * * * | 0 0 0 1  0 0 1 1 0 0 | 1 0 0 1 1
  0 1  1 | *  *  * * 10 * * | 0 0 0 0  1 0 0 1 1 0 | 0 0 1 1 1
  0 0  2 | *  *  * *  * 5 * | 0 0 1 0  0 0 0 0 1 1 | 0 1 1 0 1
  0 0  2 | *  *  * *  * * 5 | 0 0 0 0  0 1 0 1 0 1 | 0 1 0 1 1
---------+------------------+----------------------+----------
  5 0  0 | 5  0  0 0  0 0 0 | 1 * * *  * * * * * * | 1 1 0 0 0
  2 1  0 | 1  2  0 0  0 0 0 | * 5 * *  * * * * * * | 1 0 1 0 0
  2 0  2 | 1  0  2 0  0 1 0 | * * 5 *  * * * * * * | 0 1 1 0 0
  1 2  0 | 0  2  0 1  0 0 0 | * * * 5  * * * * * * | 1 0 0 1 0
  1 1  1 | 0  1  1 0  1 0 0 | * * * * 10 * * * * * | 0 0 1 1 0
  1 0  2 | 0  0  2 0  0 0 1 | * * * *  * 5 * * * * | 0 1 0 1 0
  0 5  0 | 0  0  0 5  0 0 0 | * * * *  * * 1 * * * | 1 0 0 0 1
  0 2  2 | 0  0  0 1  2 0 1 | * * * *  * * * 5 * * | 0 0 0 1 1
  0 1  2 | 0  0  0 0  2 1 0 | * * * *  * * * * 5 * | 0 0 1 0 1
  0 0 10 | 0  0  0 0  0 5 5 | * * * *  * * * * * 1 | 0 1 0 0 1
---------+------------------+----------------------+----------
♦ 5 5  0 | 5 10  0 5  0 0 0 | 1 5 0 5  0 0 1 0 0 0 | 1 * * * *
♦ 5 0 10 | 5  0 10 0  0 5 5 | 1 0 5 0  0 5 0 0 0 1 | * 1 * * *
♦ 2 1  2 | 1  2  2 0  2 1 0 | 0 1 1 0  2 0 0 0 1 0 | * * 5 * *
♦ 1 2  2 | 0  2  2 1  2 0 1 | 0 0 0 1  2 1 0 1 0 0 | * * * 5 *
♦ 0 5 10 | 0  0  0 5 10 5 5 | 0 0 0 0  0 0 1 5 5 1 | * * * * 1

© 2004-2024
top of page