Acronym pedap
Name pentagonal duoantiprism
Circumradius ...
Confer
more general:
sns2sms  
uniform relatives:
gudap  
general polytopal classes:
isogonal  
External
links
polytopewiki  

No uniform realisation is possible for any secondary edge resizement. Even so all are isogonal.

As abstract polytope pedap is isomorph to the (then uniform but non-convex) gudap, thereby replacing one cycle of pentagons by pentagrams, resp. one ring of paps by a ring of starps.


Incidence matrix according to Dynkin symbol

s5s2s5s   K = x(10,2) = sqrt[(5+sqrt(5))/2] = 1.902113

demi( . . . . ) | 50 |  1  1  1  1  2  2 |  1  1  3  3  3  3 | 1 1 1 1  4
----------------+----+-------------------+-------------------+-----------
      s 2 s .   |  2 | 25  *  *  *  *  * |  0  0  2  0  2  0 | 1 0 1 0  2  q
      s . 2 s   |  2 |  * 25  *  *  *  * |  0  0  0  2  2  0 | 0 1 1 0  2  q
      . s2s .   |  2 |  *  * 25  *  *  * |  0  0  2  0  0  2 | 1 0 0 1  2  q
      . s 2 s   |  2 |  *  *  * 25  *  * |  0  0  0  2  0  2 | 0 1 0 1  2  q
sefa( s5s . . ) |  2 |  *  *  *  * 50  * |  1  0  1  1  0  0 | 1 1 0 0  1  K
sefa( . . s5s ) |  2 |  *  *  *  *  * 50 |  0  1  0  0  1  1 | 0 0 1 1  1  K
----------------+----+-------------------+-------------------+-----------
      s5s . .   |  5 |  0  0  0  0  5  0 | 10  *  *  *  *  * | 1 1 0 0  0  K5o
      . . s5s   |  5 |  0  0  0  0  0  5 |  * 10  *  *  *  * | 0 0 1 1  0  K5o
sefa( s5s2s . ) |  3 |  1  0  1  0  1  0 |  *  * 50  *  *  * | 1 0 0 0  1  oK&#q
sefa( s5s 2 s ) |  3 |  0  1  0  1  1  0 |  *  *  * 50  *  * | 0 1 0 0  1  oK&#q
sefa( s 2 s5s ) |  3 |  1  1  0  0  0  1 |  *  *  *  * 50  * | 0 0 1 0  1  oK&#q
sefa( . s2s5s ) |  3 |  0  0  1  1  0  1 |  *  *  *  *  * 50 | 0 0 0 1  1  oK&#q
----------------+----+-------------------+-------------------+-----------
      s5s2s .   | 10 |  5  0  5  0 10  0 |  2  0 10  0  0  0 | 5 * * *  *  chiral 5ap variant
      s5s 2 s   | 10 |  0  5  0  5 10  0 |  2  0  0 10  0  0 | * 5 * *  *  chiral 5ap variant
      s 2 s5s   | 10 |  5  5  0  0  0 10 |  0  2  0  0 10  0 | * * 5 *  *  chiral 5ap variant
      . s2s5s   | 10 |  0  0  5  5  0 10 |  0  2  0  0  0 10 | * * * 5  *  chiral 5ap variant
sefa( s5s2s5s ) |  4 |  1  1  1  1  1  1 |  0  0  1  1  1  1 | * * * * 50  disphenoid (2ap)
or
demi( . . . . )   | 50 |   4  2  2 |  1  1   6   6 |  2  2  4
------------------+----+-----------+---------------+---------
      s 2 s .   & |  2 | 100  *  * |  0  0   2   2 |  1  1  2  q
sefa( s5s . . )   |  2 |   * 50  * |  1  0   2   0 |  2  0  1  K
sefa( . . s5s )   |  2 |   *  * 50 |  0  1   0   2 |  0  2  1  K
------------------+----+-----------+---------------+---------
      s5s . .     |  5 |   0  5  0 | 10  *   *   * |  2  0  0  K5o
      . . s5s     |  5 |   0  0  5 |  * 10   *   * |  0  2  0  K5o
sefa( s5s2s . ) & |  3 |   2  1  0 |  *  * 100   * |  1  0  1  oK&#q
sefa( s 2 s5s ) & |  3 |   2  0  1 |  *  *   * 100 |  0  1  1  oK&#q
------------------+----+-----------+---------------+---------
      s5s2s .   & | 10 |  10 10  0 |  2  0  10   0 | 10  *  *  chiral 5ap variant
      s 2 s5s   & | 10 |  10  0 10 |  0  2   0  10 |  * 10  *  chiral 5ap variant
sefa( s5s2s5s )   |  4 |   4  1  1 |  0  0   2   2 |  *  * 50  disphenoid (2ap)

starting figure: x5x x5x

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