Acronym phiddip
Name pentagon hexagon duoprism
 
Circumradius sqrt[(15+sqrt(5))/10] = 1.312862
Volume 3 sqrt[75+30 sqrt(5)]/8 = 4.469931
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {5} between pip and pip:   120°
  • at {6} between hip and hip:   108°
  • at {4} between hip and pip:   90°
Face vector 30, 60, 41, 11
Confer
general duoprisms:
5,n-dip   6,n-dip   n,m-dip   2n,m-dip  
general polytopal classes:
bistratic lace towers  
External
links 		hedrondude   wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

x5o x6o

. . . . | 30 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 30  * | 1  2 0 | 2 1
. . x . |  2 |  * 30 | 0  2 1 | 1 2
--------+----+-------+--------+----
x5o . . |  5 |  5  0 | 6  * * | 2 0
x . x . |  4 |  2  2 | * 30 * | 1 1
. . x6o |  6 |  0  6 | *  * 5 | 0 2
--------+----+-------+--------+----
x5o x . ♦ 10 | 10  5 | 2  5 0 | 6 *
x . x6o ♦ 12 |  6 12 | 0  6 2 | * 5


x5o x6/5o

. . .   . | 30 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 30  * | 1  2 0 | 2 1
. . x   . |  2 |  * 30 | 0  2 1 | 1 2
----------+----+-------+--------+----
x5o .   . |  5 |  5  0 | 6  * * | 2 0
x . x   . |  4 |  2  2 | * 30 * | 1 1
. . x6/5o |  6 |  0  6 | *  * 5 | 0 2
----------+----+-------+--------+----
x5o x   . ♦ 10 | 10  5 | 2  5 0 | 6 *
x . x6/5o ♦ 12 |  6 12 | 0  6 2 | * 5


x5/4o x6o

.   . . . | 30 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x   . . . |  2 | 30  * | 1  2 0 | 2 1
.   . x . |  2 |  * 30 | 0  2 1 | 1 2
----------+----+-------+--------+----
x5/4o . . |  5 |  5  0 | 6  * * | 2 0
x   . x . |  4 |  2  2 | * 30 * | 1 1
.   . x6o |  6 |  0  6 | *  * 5 | 0 2
----------+----+-------+--------+----
x5/4o x . ♦ 10 | 10  5 | 2  5 0 | 6 *
x   . x6o ♦ 12 |  6 12 | 0  6 2 | * 5


x5/4o x6/5o

.   . .   . | 30 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 30  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 30 | 0  2 1 | 1 2
------------+----+-------+--------+----
x5/4o .   . |  5 |  5  0 | 6  * * | 2 0
x   . x   . |  4 |  2  2 | * 30 * | 1 1
.   . x6/5o |  6 |  0  6 | *  * 5 | 0 2
------------+----+-------+--------+----
x5/4o x   . ♦ 10 | 10  5 | 2  5 0 | 6 *
x   . x6/5o ♦ 12 |  6 12 | 0  6 2 | * 5


x3x x5o

. . . . | 30 |  1  1  2 | 1  2  2 1 | 2 1 1
--------+----+----------+-----------+------
x . . . |  2 | 15  *  * | 1  2  0 0 | 2 1 0
. x . . |  2 |  * 15  * | 1  0  2 0 | 2 0 1
. . x . |  2 |  *  * 30 | 0  1  1 1 | 1 1 1
--------+----+----------+-----------+------
x3x . . |  6 |  3  3  0 | 5  *  * * | 2 0 0
x . x . |  4 |  2  0  2 | * 15  * * | 1 1 0
. x x . |  4 |  0  2  2 | *  * 15 * | 1 0 1
. . x5o |  n |  0  0  n | *  *  * 6 | 0 1 1
--------+----+----------+-----------+------
x3x x . ♦ 12 |  6  6  6 | 2  3  3 0 | 5 * *
x . x5o ♦ 10 |  5  0 10 | 0  5  0 2 | * 3 *
. x x5o ♦ 10 |  0  5 10 | 0  0  5 2 | * * 3


x3x x5/4o

. . .   . | 30 |  1  1  2 | 1  2  2 1 | 2 1 1
----------+----+----------+-----------+------
x . .   . |  2 | 15  *  * | 1  2  0 0 | 2 1 0
. x .   . |  2 |  * 15  * | 1  0  2 0 | 2 0 1
. . x   . |  2 |  *  * 30 | 0  1  1 1 | 1 1 1
----------+----+----------+-----------+------
x3x .   . |  6 |  3  3  0 | 5  *  * * | 2 0 0
x . x   . |  4 |  2  0  2 | * 15  * * | 1 1 0
. x x   . |  4 |  0  2  2 | *  * 15 * | 1 0 1
. . x5/4o |  n |  0  0  n | *  *  * 6 | 0 1 1
----------+----+----------+-----------+------
x3x x   . ♦ 12 |  6  6  6 | 2  3  3 0 | 5 * *
x . x5/4o ♦ 10 |  5  0 10 | 0  5  0 2 | * 3 *
. x x5/4o ♦ 10 |  0  5 10 | 0  0  5 2 | * * 3


xux xxx5ooo&#xt   → both heights = sqrt(3)/2 = 0.866025
(pip || pseudo (x,u)-pip || n-p)

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

or
o.. o..5o..      & | 20  * |  1  2  1  0 |  2 1  2 1 0 | 1 1 2
.o. .o.5.o.        |  * 10 |  0  0  2  2 |  0 0  4 1 1 | 0 2 2
-------------------+-------+-------------+-------------+------
x.. ... ...      & |  2  0 | 10  *  *  * |  2 0  0 1 0 | 1 0 2
... x.. ...      & |  2  0 |  * 20  *  * |  1 1  1 0 0 | 1 1 1
oo. oo.5oo.&#x   & |  1  1 |  *  * 20  * |  0 0  2 1 0 | 0 1 2
... .x. ...        |  0  2 |  *  *  * 10 |  0 0  2 0 1 | 0 2 1
-------------------+-------+-------------+-------------+------
x.. x.. ...      & |  4  0 |  2  2  0  0 | 10 *  * * * | 1 0 1
... x..5o..      & |  5  0 |  0  5  0  0 |  * 4  * * * | 1 1 0
... xx. ...&#x   & |  2  2 |  0  1  2  1 |  * * 20 * * | 0 1 1
xux ... ...&#xt    |  4  2 |  2  0  4  0 |  * *  * 5 * | 0 0 2
... .x.5.o.        |  0  5 |  0  0  0  5 |  * *  * * 2 | 0 2 0
-------------------+-------+-------------+-------------+------
x.. x..5o..      & ♦ 10  0 |  5 10  0  0 |  5 2  0 0 0 | 2 * *
... xx.5oo.&#x   & ♦  5  5 |  0  5  5  5 |  0 1  5 0 1 | * 4 *
xux xxx ...&#xt    ♦  8  4 |  4  4  8  2 |  2 0  4 2 0 | * * 5


ofx xxx6ooo&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                    height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({6} || pseudo (f,x)-hip || hip)

o.. o..6o..     | 6  *  * | 2  2  0  0 0  0 | 1 1  4 0  0 0 0 | 2 2 0 0
.o. .o.6.o.     | * 12  * | 0  1  2  1 0  0 | 0 1  2 1  2 0 0 | 2 1 1 0
..o ..o6..o     | *  * 12 | 0  0  0  1 1  2 | 0 1  0 0  2 2 1 | 2 0 1 1
----------------+---------+-----------------+-----------------+--------
... x.. ...     | 2  0  0 | 6  *  *  * *  * | 1 0  2 0  0 0 0 | 1 2 0 0
oo. oo.6oo.&#x  | 1  1  0 | * 12  *  * *  * | 0 1  2 0  0 0 0 | 2 1 0 0
... .x. ...     | 0  2  0 | *  * 12  * *  * | 0 0  1 1  1 0 0 | 1 1 1 0
.oo .oo6.oo&#x  | 0  1  1 | *  *  * 12 *  * | 0 1  0 0  2 0 0 | 2 0 1 0
..x ... ...     | 0  0  2 | *  *  *  * 6  * | 0 1  0 0  0 2 0 | 2 0 0 1
... ..x ...     | 0  0  2 | *  *  *  * * 12 | 0 0  0 0  1 1 1 | 1 0 1 1
----------------+---------+-----------------+-----------------+--------
... x..6o..     | 6  0  0 | 6  0  0  0 0  0 | 1 *  * *  * * * | 0 2 0 0
ofx ... ...&#xt | 1  2  2 | 0  2  0  2 1  0 | * 6  * *  * * * | 2 0 0 0
... xx. ...&#x  | 2  2  0 | 1  2  1  0 0  0 | * * 12 *  * * * | 1 1 0 0
... .x.6.o.     | 0  6  0 | 0  0  6  0 0  0 | * *  * 2  * * * | 0 1 1 0
... .xx ...&#x  | 0  2  2 | 0  0  1  2 0  1 | * *  * * 12 * * | 1 0 1 0
..x ..x ...     | 0  0  4 | 0  0  0  0 2  2 | * *  * *  * 6 * | 1 0 0 1
... ..x6..o     | 0  0  6 | 0  0  0  0 0  6 | * *  * *  * * 2 | 0 0 1 1
----------------+---------+-----------------+-----------------+--------
ofx xxx ...&#xt ♦ 2  4  4 | 1  4  2  4 2  2 | 0 2  2 0  2 1 0 | 6 * * *
... xx.6oo.&#x  ♦ 6  6  0 | 6  6  6  0 0  0 | 1 0  6 1  0 0 0 | * 2 * *
... .xx6.oo&#x  ♦ 0  6  6 | 0  0  6  6 0  6 | 0 0  0 1  6 0 1 | * * 2 *
..x ..x6..o     ♦ 0  0 12 | 0  0  0  0 6 12 | 0 0  0 0  0 6 2 | * * * 1


ofx xxx3xxx&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                    height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({6} || pseudo (f,x)-hip || hip)

o.. o..3o..     | 6  *  * | 1 1  2 0 0  0 0 0 0 | 1 1 2 2 0 0 0 0 0 0 | 1 1 2 0 0
.o. .o.3.o.     | * 12  * | 0 0  1 1 1  1 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
..o ..o3..o     | *  * 12 | 0 0  0 0 0  1 1 1 1 | 0 1 0 0 0 1 1 1 1 1 | 1 1 0 1 1
----------------+---------+---------------------+---------------------+----------
... x.. ...     | 2  0  0 | 3 *  * * *  * * * * | 1 0 2 0 0 0 0 0 0 0 | 1 0 2 0 0
... ... x..     | 2  0  0 | * 3  * * *  * * * * | 1 0 0 2 0 0 0 0 0 0 | 0 1 2 0 0
oo. oo.3oo.&#x  | 1  1  0 | * * 12 * *  * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
... .x. ...     | 0  2  0 | * *  * 6 *  * * * * | 0 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0
... ... .x.     | 0  2  0 | * *  * * 6  * * * * | 0 0 0 1 1 0 1 0 0 0 | 0 1 1 1 0
.oo .oo3.oo&#x  | 0  1  1 | * *  * * * 12 * * * | 0 1 0 0 0 1 1 0 0 0 | 1 1 0 1 0
..x ... ...     | 0  0  2 | * *  * * *  * 6 * * | 0 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1
... ..x ...     | 0  0  2 | * *  * * *  * * 6 * | 0 0 0 0 0 1 0 1 0 1 | 1 0 0 1 1
... ... ..x     | 0  0  2 | * *  * * *  * * * 6 | 0 0 0 0 0 0 1 0 1 1 | 0 1 0 1 1
----------------+---------+---------------------+---------------------+----------
... x..3x..     | 6  0  0 | 3 3  0 0 0  0 0 0 0 | 1 * * * * * * * * * | 0 0 2 0 0
ofx ... ...&#xt | 1  2  2 | 0 0  2 0 0  2 1 0 0 | * 6 * * * * * * * * | 1 1 0 0 0
... xx. ...&#x  | 2  2  0 | 1 0  2 1 0  0 0 0 0 | * * 6 * * * * * * * | 1 0 1 0 0
... ... xx.&#x  | 2  2  0 | 0 1  2 0 1  0 0 0 0 | * * * 6 * * * * * * | 0 1 1 0 0
... .x.3.x.     | 0  6  0 | 0 0  0 3 3  0 0 0 0 | * * * * 2 * * * * * | 0 0 1 1 0
... .xx ...&#x  | 0  2  2 | 0 0  0 1 0  2 0 1 0 | * * * * * 6 * * * * | 1 0 0 1 0
... ... .xx&#x  | 0  2  2 | 0 0  0 0 1  2 0 0 1 | * * * * * * 6 * * * | 0 1 0 1 0
..x ..x ...     | 0  0  4 | 0 0  0 0 0  0 2 2 0 | * * * * * * * 3 * * | 1 0 0 0 1
..x ... ..x     | 0  0  4 | 0 0  0 0 0  0 2 0 2 | * * * * * * * * 3 * | 0 1 0 0 1
... ..x3..x     | 0  0  6 | 0 0  0 0 0  0 0 3 3 | * * * * * * * * * 2 | 0 0 0 1 1
----------------+---------+---------------------+---------------------+----------
ofx xxx ...&#xt ♦ 2  4  4 | 1 0  4 2 0  4 2 2 0 | 0 2 2 0 0 2 0 1 0 0 | 3 * * * *
ofx ... xxx&#xt ♦ 2  4  4 | 0 1  4 0 2  4 2 0 2 | 0 2 0 2 0 0 2 0 1 0 | * 3 * * *
... xx.3xx.&#x  ♦ 6  6  0 | 3 3  6 3 3  0 0 0 0 | 1 0 3 3 1 0 0 0 0 0 | * * 2 * *
... .xx3.xx&#x  ♦ 0  6  6 | 0 0  0 3 3  6 0 3 3 | 0 0 0 0 1 3 3 0 0 1 | * * * 2 *
..x ..x3..x     ♦ 0  0 12 | 0 0  0 0 0  0 6 6 6 | 0 0 0 0 0 0 0 3 3 2 | * * * * 1

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