Acronym	pap
TOCID symbol	(5)Q
Name	pentagonal antiprism, para-bidiminished icosahedron
	© ©
Circumradius	sqrt[(5+sqrt(5))/8] = 0.951057
Vertex figure	[33,5]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {3}:   arccos(-sqrt(5)/3) = 138.189685° between {3} and {5}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
Dual	p2p5p
Face vector	10, 20, 12
Confer	general antiprisms: n-ap   n/2-ap   n/d-ap   uniform relative: ike   faceting of: ike   blends: 2 pap blend   compounds: gassid   gadsid   general polytopal classes: segmentohedra   fundamental lace prisms
External links

This polyhedron is an edge-faceting of the icosahedron (ike).

Incidence matrix according to Dynkin symbol

s2s5s

demi( . . .  ) | 10 | 1 1  2 | 1  3
---------------+----+--------+-----
      s2s .    |  2 | 5 *  * | 0  2
      s . s2*a |  2 | * 5  * | 0  2
sefa( . s5s  ) |  2 | * * 10 | 1  1
---------------+----+--------+-----
      . s5s    ♦  5 | 0 0  5 | 2  *
sefa( s2s5s  ) |  3 | 1 1  1 | * 10

starting figure: x x5x

s2s10o

demi( . .  . ) | 10 |  2  2 | 1  3
---------------+----+-------+-----
      s2s  .   |  2 | 10  * | 0  2
sefa( . s10o ) |  2 |  * 10 | 1  1
---------------+----+-------+-----
      . s10o   ♦  5 |  0  5 | 2  *
sefa( s2s10o ) |  3 |  2  1 | * 10

starting figure: x x10o

xo5ox&#x   → height = sqrt[(5+sqrt(5))/10] = 0.850651
({5} || dual {5})

o.5o.    | 5 * | 2  2 0 | 1 2 1 0
.o5.o    | * 5 | 0  2 2 | 0 1 2 1
---------+-----+--------+--------
x. ..    | 2 0 | 5  * * | 1 1 0 0
oo5oo&#x | 1 1 | * 10 * | 0 1 1 0
.. .x    | 0 2 | *  * 5 | 0 0 1 1
---------+-----+--------+--------
x.5o.    | 5 0 | 5  0 0 | 1 * * *
xo ..&#x | 2 1 | 1  2 0 | * 5 * *
.. ox&#x | 1 2 | 0  2 1 | * * 5 *
.o5.x    | 0 5 | 0  0 5 | * * * 1