Acronym ...
Name blend of 2 pentagonal antiprisms,
pair of pentagonal butterfly wedges
 
Circumradius sqrt[(5+sqrt(5))/8] = 0.951057
Vertex figure [33,5], [3,5,3/2,5/4], and [34,5/42] (type B)
[33,5], [3,5,3/2,5/4], and [32,5,3/22,5/4] (type C)
[33,5], [3,5,3/2,5/4], and [32,5] (type D)
Lace city
in approx. ASCII-art
 o   o 
   f   
x     x
   f   
 o   o 
Coordinates (τ/2, 1/2, 0)   & even permutations, all changes of sign
where τ = (1+sqrt(5))/2
Dihedral angles
(at margins)
  • between {3} and {3}:   arccos(-sqrt(5)/3) = 138.189685°
  • between {3} and {5} (of pap):   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
  • between {3} and {5} (of peppy):   arccos(sqrt[(5+2 sqrt(5))/15]) = 37.377368°
Confer
uniform relatives:
ike  
blend-component:
pap   peppy  
compound-component:
2peppy-blend  

Comes in serveral types: either there will be tetravelent edges (type A), thus conflicting to dydicity, or those vertices still would be identified, but the edges will be considered a pair of completely coincident ones. Then the figure clearly is exotic. Here there are still 2 types to be considered: either 2 adjacent triangles connect at one of these edges while 2 pentagons would connect at the other (type B), or at either edge there would be one triangle and one pentagon in the way those were connected in the pap (type C).

Finally there is an interpretation of this figure (type D) as a compound of 2 2peppy-blends, resulting in both, pairs of coincident edges and pairs of coincident vertices. Then again one triangle and one pentagon each is incident to these edges under consideration, but in the way those were connected in the base edge of peppy.


Incidence matrix

(Type A)

4 * * | 1 2 2 0 | 2 2 2  : x o  &
* 4 * | 0 2 0 2 | 1 2 1  : o f  &
* * 4 | 0 0 2 2 | 0 2 2  : f x  &
------+---------+------
2 0 0 | 2 * * * | 2 0 2
1 1 0 | * 8 * * | 1 1 0
1 0 1 | * * 8 * | 0 1 1
0 1 1 | * * * 8 | 0 1 1
------+---------+------
2 1 0 | 1 2 0 0 | 4 * *
1 1 1 | 0 1 1 1 | * 8 *
2 1 2 | 1 0 2 2 | * * 4

(Type B)

4 * * | 1 1 2 2 0 | 2 2 2  : x o  &
* 4 * | 0 0 2 0 2 | 1 2 1  : o f  &
* * 4 | 0 0 0 2 2 | 0 2 2  : f x  &
------+-----------+------
2 0 0 | 2 * * * * | 2 0 0
2 0 0 | * 2 * * * | 0 0 2
1 1 0 | * * 8 * * | 1 1 0
1 0 1 | * * * 8 * | 0 1 1
0 1 1 | * * * * 8 | 0 1 1
------+-----------+------
2 1 0 | 1 0 2 0 0 | 4 * *
1 1 1 | 0 0 1 1 1 | * 8 *
2 1 2 | 0 1 0 2 2 | * * 4

(Type C)

4 * * | 1 2 2 0 | 2 2 2  : x o  &
* 4 * | 0 2 0 2 | 1 2 1  : o f  &
* * 4 | 0 0 2 2 | 0 2 2  : f x  &
------+---------+------
2 0 0 | 4 * * * | 1 0 1
1 1 0 | * 8 * * | 1 1 0
1 0 1 | * * 8 * | 0 1 1
0 1 1 | * * * 8 | 0 1 1
------+---------+------
2 1 0 | 1 2 0 0 | 4 * *
1 1 1 | 0 1 1 1 | * 8 *
2 1 2 | 1 0 2 2 | * * 4

(Type D)

4 * * | 1 2 2 0 | 2 2 2 || 2  : x o  &
* 4 * | 0 2 0 2 | 1 2 1 || 1  : o f  &
* * 4 | 0 0 2 2 | 0 2 2 || 1  : f x  &
------+---------+-------++--
2 0 0 | 2 * * * | 1 0 1 || 2
1 1 0 | * 8 * * | 1 1 0 || 1
1 0 1 | * * 8 * | 0 1 1 || 1
0 1 1 | * * * 8 | 0 1 1 || 1
------+---------+-------++--
2 1 0 | 1 2 0 0 | 4 * * || 1
1 1 1 | 0 1 1 1 | * 8 * || 1
2 1 2 | 1 0 2 2 | * * 4 || 1
------+---------+-------++--
4 2 2 | 2 4 4 4 | 2 4 2 || 2  : 2peppy-blend

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