Acronym pedip
Name pentagon-pentagon duoprism
  ©  
Circumradius sqrt[1+1/sqrt(5)] = 1.203002
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {5} between pip and pip:   108°
  • at {4} between pip and pip:   90°
Confer
general duoprisms:
n,n-dip   n,m-dip   5,n-dip  
general polytopal classes:
noble polytopes   bistratic lace towers  
External
links
hedrondude   wikipedia

Note that pedip can be thought of as the external blend of 5 pippies + 5 pescs + 5 pafs. This decomposition is described as the degenerate segmentoteron ox5oo ox5xo&#xt.


Incidence matrix according to Dynkin symbol

x5o x5o

. . . . | 25 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 25  * | 1  2 0 | 2 1
. . x . |  2 |  * 25 | 0  2 1 | 1 2
--------+----+-------+--------+----
x5o . . |  5 |  5  0 | 5  * * | 2 0
x . x . |  4 |  2  2 | * 25 * | 1 1
. . x5o |  5 |  0  5 | *  * 5 | 0 2
--------+----+-------+--------+----
x5o x .  10 | 10  5 | 2  5 0 | 5 *
x . x5o  10 |  5 10 | 0  5 2 | * 5
or
. . . .    | 25 |  4 |  2  4 |  4
-----------+----+----+-------+---
x . . .  & |  2 | 50 |  1  2 |  3
-----------+----+----+-------+---
x5o . .  & |  5 |  5 | 10  * |  2
x . x .    |  4 |  4 |  * 25 |  2
-----------+----+----+-------+---
x5o x .  &  10 | 15 |  2  5 | 10

x5o x5/4o

. . .   . | 25 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 25  * | 1  2 0 | 2 1
. . x   . |  2 |  * 25 | 0  2 1 | 1 2
----------+----+-------+--------+----
x5o .   . |  5 |  5  0 | 5  * * | 2 0
x . x   . |  4 |  2  2 | * 25 * | 1 1
. . x5/4o |  5 |  0  5 | *  * 5 | 0 2
----------+----+-------+--------+----
x5o x   .  10 | 10  5 | 2  5 0 | 5 *
x . x5/4o  10 |  5 10 | 0  5 2 | * 5

x5/4o x5/4o

.   . .   . | 25 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 25  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 25 | 0  2 1 | 1 2
------------+----+-------+--------+----
x5/4o .   . |  5 |  5  0 | 5  * * | 2 0
x   . x   . |  4 |  2  2 | * 25 * | 1 1
.   . x5/4o |  5 |  0  5 | *  * 5 | 0 2
------------+----+-------+--------+----
x5/4o x   .  10 | 10  5 | 2  5 0 | 5 *
x   . x5/4o  10 |  5 10 | 0  5 2 | * 5
or
.   . .   .    | 25 |  4 |  2  4 |  4
---------------+----+----+-------+---
x   . .   .  & |  2 | 50 |  1  2 |  3
---------------+----+----+-------+---
x5/4o .   .  & |  5 |  5 | 10  * |  2
x   . x   .    |  4 |  4 |  * 25 |  2
---------------+----+----+-------+---
x5/4o x   .  &  10 | 15 |  2  5 | 10

ofx xxx5ooo&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                    height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({5} || pseudo (f,x)-pip || pip)

o.. o..5o..     | 5  *  * | 2  2  0  0 0  0 | 1 1  4 0  0 0 0 | 2 2 0 0
.o. .o.5.o.     | * 10  * | 0  1  2  1 0  0 | 0 1  2 1  2 0 0 | 2 1 1 0
..o ..o5..o     | *  * 10 | 0  0  0  1 1  2 | 0 1  0 0  2 2 1 | 2 0 1 1
----------------+---------+-----------------+-----------------+--------
... x.. ...     | 2  0  0 | 5  *  *  * *  * | 1 0  2 0  0 0 0 | 1 2 0 0
oo. oo.5oo.&#x  | 1  1  0 | * 10  *  * *  * | 0 1  2 0  0 0 0 | 2 1 0 0
... .x. ...     | 0  2  0 | *  * 10  * *  * | 0 0  1 1  1 0 0 | 1 1 1 0
.oo .oo5.oo&#x  | 0  1  1 | *  *  * 10 *  * | 0 1  0 0  2 0 0 | 2 0 1 0
..x ... ...     | 0  0  2 | *  *  *  * 5  * | 0 1  0 0  0 2 0 | 2 0 0 1
... ..x ...     | 0  0  2 | *  *  *  * * 10 | 0 0  0 0  1 1 1 | 1 0 1 1
----------------+---------+-----------------+-----------------+--------
... x..5o..     | 5  0  0 | 5  0  0  0 0  0 | 1 *  * *  * * * | 0 2 0 0
ofx ... ...&#xt | 1  2  2 | 0  2  0  2 1  0 | * 5  * *  * * * | 2 0 0 0
... xx. ...&#x  | 2  2  0 | 1  2  1  0 0  0 | * * 10 *  * * * | 1 1 0 0
... .x.5.o.     | 0  5  0 | 0  0  5  0 0  0 | * *  * 2  * * * | 0 1 1 0
... .xx ...&#x  | 0  2  2 | 0  0  1  2 0  1 | * *  * * 10 * * | 1 0 1 0
..x ..x ...     | 0  0  4 | 0  0  0  0 2  2 | * *  * *  * 5 * | 1 0 0 1
... ..x5..o     | 0  0  5 | 0  0  0  0 0  5 | * *  * *  * * 2 | 0 0 1 1
----------------+---------+-----------------+-----------------+--------
ofx xxx ...&#xt  2  4  4 | 1  4  2  4 2  2 | 0 2  2 0  2 1 0 | 5 * * *
... xx.5oo.&#x   5  5  0 | 5  5  5  0 0  0 | 1 0  5 1  0 0 0 | * 2 * *
... .xx5.oo&#x   0  5  5 | 0  0  5  5 0  5 | 0 0  0 1  5 0 1 | * * 2 *
..x ..x5..o      0  0 10 | 0  0  0  0 5 10 | 0 0  0 0  0 5 2 | * * * 1

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