Acronym	pedap
Name	pentagonal duoantiprism
Circumradius	...
Face vector	50, 200, 220, 70
Confer	more general: sns2sms   uniform relatives: gudap   general polytopal classes: isogonal
External links

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