Acronym	...
Name	pentagonal antidipyramid, pentagonal antitegum, pentagonal kiteohedron, dual of pap, axial bi-kis-doe, deca-truncated sissid
	©
Vertex figure	[k5], [K3]
Dihedral angles	at long edge:   arccos(-1/sqrt(5)) = 116.565051° at short edge:   arccos(-1/sqrt(5)) = 116.565051°
Dual	pap
Face vector	12, 20, 10
Confer	uniform relative: doe   sissid   general polytopal classes: Catalan polyhedra
External links

Despite the general namings above, only the dual or the kis operation settle the relative height to width ratio. All the measures provided herein will refer to that choice.

The face is kite {(k,K,K,K)} with corner angle k = 36° and K = 108°, where side KK has size v = (sqrt(5)-1)/2 = 0.618034, diagonal KK has size x = 1, side kK has size f = (1+sqrt(5))/2 = 1.618034, and diagonal kK has size sqrt[(5+sqrt(5))/2] = 1.902113.

This polyhedron can also be obtained as a stellation of doe by blending at 2 opposite pentagons with tall pyramids, which are the tips of sissid. Alternatively it is also the according deca-truncation of the latter.

Incidence matrix according to Dynkin symbol

oxoo5ooxo&#(f,v,f)t   → height(1,2) = height(3,4) = sqrt[(5+2 sqrt(5))/5] = 1.376382
                        height(2,3) = sqrt[(5-2 sqrt(5))/5] = 0.324920

o...5o...         | 1 * * * | 5  0 0 | 5 0  [k5]
.o..5.o..         | * 5 * * | 1  2 0 | 2 1  [K3]
..o.5..o.         | * * 5 * | 0  2 1 | 1 2  [K3]
...o5...o         | * * * 1 | 0  0 5 | 0 5  [k5]
------------------+---------+--------+----
oo..5oo..&#f      | 1 1 0 0 | 5  * * | 2 0
.oo.5.oo.&#v      | 0 1 1 0 | * 10 * | 1 1
..oo5..oo&#f      | 0 0 1 1 | *  * 5 | 0 2
------------------+---------+--------+----
oxo. ....&#(f,v)t | 1 2 1 0 | 2  2 0 | 5 *  {(k,K,K,K)}
.... .oxo&#(v,f)t | 0 1 2 1 | 0  2 2 | * 5  {(k,K,K,K)}

or
o...5o...         & | 2  * |  5  0 |  5  [k5]
.o..5.o..         & | * 10 |  1  2 |  3  [K3]
--------------------+------+-------+---
oo..5oo..&#f      & | 1  1 | 10  * |  2
.oo.5.oo.&#v        | 0  2 |  * 10 |  2
--------------------+------+-------+---
oxo. ....&#(v,f)t & | 1  3 |  2  2 | 10  {(k,K,K,K)}