Acronym hadedip
Name hexagon - decagon duoprism
Circumradius sqrt[(5+sqrt(5))/2] = 1.902113
Volume 15 sqrt[15+6 sqrt(5)]/4 = 19.990141
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {6} between hip and hip:   144°
  • at {10} between dip and dip:   120°
  • at {4} between dip and hip:   90°
Face vector 60, 120, 76, 16
Confer
general duoprisms:
n,m-dip   2n,m-dip   2n,2m-dip   6,n-dip   10,n-dip  
general polytopal classes:
bistratic lace towers  
External
links 		hedrondude   wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

x6o x10o

. . .  . | 60 |  2  2 |  1  4 1 |  2 2
---------+----+-------+---------+-----
x . .  . |  2 | 60  * |  1  2 0 |  2 1
. . x  . |  2 |  * 60 |  0  2 1 |  1 2
---------+----+-------+---------+-----
x6o .  . |  6 |  6  0 | 10  * * |  2 0
x . x  . |  4 |  2  2 |  * 60 * |  1 1
. . x10o | 10 |  0 10 |  *  * 6 |  0 2
---------+----+-------+---------+-----
x6o x  . ♦ 12 | 12  6 |  2  6 0 | 10 *
x . x10o ♦ 20 | 10 20 |  0 10 2 |  * 6


x6o x10/9o

. . .    . | 60 |  2  2 |  1  4 1 |  2 2
-----------+----+-------+---------+-----
x . .    . |  2 | 60  * |  1  2 0 |  2 1
. . x    . |  2 |  * 60 |  0  2 1 |  1 2
-----------+----+-------+---------+-----
x6o .    . |  6 |  6  0 | 10  * * |  2 0
x . x    . |  4 |  2  2 |  * 60 * |  1 1
. . x10/9o | 10 |  0 10 |  *  * 6 |  0 2
-----------+----+-------+---------+-----
x6o x    . ♦ 12 | 12  6 |  2  6 0 | 10 *
x . x10/9o ♦ 20 | 10 20 |  0 10 2 |  * 6


x6/5o x10o

.   . .  . | 60 |  2  2 |  1  4 1 |  2 2
-----------+----+-------+---------+-----
x   . .  . |  2 | 60  * |  1  2 0 |  2 1
.   . x  . |  2 |  * 60 |  0  2 1 |  1 2
-----------+----+-------+---------+-----
x6/5o .  . |  6 |  6  0 | 10  * * |  2 0
x   . x  . |  4 |  2  2 |  * 60 * |  1 1
.   . x10o | 10 |  0 10 |  *  * 6 |  0 2
-----------+----+-------+---------+-----
x6/5o x  . ♦ 12 | 12  6 |  2  6 0 | 10 *
x   . x10o ♦ 20 | 10 20 |  0 10 2 |  * 6


x6/5o x10/9o

.   . .    . | 60 |  2  2 |  1  4 1 |  2 2
-------------+----+-------+---------+-----
x   . .    . |  2 | 60  * |  1  2 0 |  2 1
.   . x    . |  2 |  * 60 |  0  2 1 |  1 2
-------------+----+-------+---------+-----
x6/5o .    . |  6 |  6  0 | 10  * * |  2 0
x   . x    . |  4 |  2  2 |  * 60 * |  1 1
.   . x10/9o | 10 |  0 10 |  *  * 6 |  0 2
-------------+----+-------+---------+-----
x6/5o x    . ♦ 12 | 12  6 |  2  6 0 | 10 *
x   . x10/9o ♦ 20 | 10 20 |  0 10 2 |  * 6


x3x x10o

. . .  . | 60 |  1  1  2 |  1  2  2 1 |  2 1 1
---------+----+----------+------------+-------
x . .  . |  2 | 30  *  * |  1  2  0 0 |  2 1 0
. x .  . |  2 |  * 30  * |  1  0  2 0 |  2 0 1
. . x  . |  2 |  *  * 60 |  0  1  1 1 |  1 1 1
---------+----+----------+------------+-------
x3x .  . |  6 |  3  3  0 | 10  *  * * |  2 0 0
x . x  . |  4 |  2  0  2 |  * 30  * * |  1 1 0
. x x  . |  4 |  0  2  2 |  *  * 30 * |  1 0 1
. . x10o | 10 |  0  0 10 |  *  *  * 6 |  0 1 1
---------+----+----------+------------+-------
x3x x  . ♦ 12 |  6  6  6 |  2  3  3 0 | 10 * *
x . x10o ♦ 20 | 10  0 20 |  0 10  0 2 |  * 3 *
. x x10o ♦ 20 |  0 10 20 |  0  0 10 2 |  * * 3


x3x x10/9o

. . .    . | 60 |  1  1  2 |  1  2  2 1 |  2 1 1
-----------+----+----------+------------+-------
x . .    . |  2 | 30  *  * |  1  2  0 0 |  2 1 0
. x .    . |  2 |  * 30  * |  1  0  2 0 |  2 0 1
. . x    . |  2 |  *  * 60 |  0  1  1 1 |  1 1 1
-----------+----+----------+------------+-------
x3x .    . |  6 |  3  3  0 | 10  *  * * |  2 0 0
x . x    . |  4 |  2  0  2 |  * 30  * * |  1 1 0
. x x    . |  4 |  0  2  2 |  *  * 30 * |  1 0 1
. . x10/9o | 10 |  0  0 10 |  *  *  * 6 |  0 1 1
-----------+----+----------+------------+-------
x3x x    . ♦ 12 |  6  6  6 |  2  3  3 0 | 10 * *
x . x10/9o ♦ 20 | 10  0 20 |  0 10  0 2 |  * 3 *
. x x10/9o ♦ 20 |  0 10 20 |  0  0 10 2 |  * * 3


x5x x6o

. . . . | 60 |  1  1  2 | 1  2  2  1 | 2 1 1
--------+----+----------+------------+------
x . . . |  2 | 30  *  * | 1  2  0  0 | 2 1 0
. x . . |  2 |  * 30  * | 1  0  2  0 | 2 0 1
. . x . |  2 |  *  * 60 | 0  1  1  1 | 1 1 1
--------+----+----------+------------+------
x5x . . | 10 |  5  5  0 | 6  *  *  * | 2 0 0
x . x . |  4 |  2  0  2 | * 30  *  * | 1 1 0
. x x . |  4 |  0  2  2 | *  * 30  * | 1 0 1
. . x6o |  6 |  0  0  6 | *  *  * 10 | 0 1 1
--------+----+----------+------------+------
x5x x . ♦ 20 | 10 10 10 | 2  5  5  0 | 6 * *
x . x6o ♦ 12 |  6  0 12 | 0  6  0  2 | * 5 *
. x x6o ♦ 12 |  0  6 12 | 0  0  6  2 | * * 5


x5x x6/5o

. . .   . | 60 |  1  1  2 | 1  2  2  1 | 2 1 1
----------+----+----------+------------+------
x . .   . |  2 | 30  *  * | 1  2  0  0 | 2 1 0
. x .   . |  2 |  * 30  * | 1  0  2  0 | 2 0 1
. . x   . |  2 |  *  * 60 | 0  1  1  1 | 1 1 1
----------+----+----------+------------+------
x5x .   . | 10 |  5  5  0 | 6  *  *  * | 2 0 0
x . x   . |  4 |  2  0  2 | * 30  *  * | 1 1 0
. x x   . |  4 |  0  2  2 | *  * 30  * | 1 0 1
. . x6/5o |  6 |  0  0  6 | *  *  * 10 | 0 1 1
----------+----+----------+------------+------
x5x x   . ♦ 20 | 10 10 10 | 2  5  5  0 | 6 * *
x . x6/5o ♦ 12 |  6  0 12 | 0  6  0  2 | * 5 *
. x x6/5o ♦ 12 |  0  6 12 | 0  0  6  2 | * * 5


x3x x5x

. . . . | 60 |  1  1  1  1 |  1  1  1  1  1 1 | 1 1 1 1
--------+----+-------------+------------------+--------
x . . . |  2 | 30  *  *  * |  1  1  1  0  0 0 | 1 1 1 0
. x . . |  2 |  * 30  *  * |  1  0  0  1  1 0 | 1 1 0 1
. . x . |  2 |  *  * 30  * |  0  1  0  1  0 1 | 1 0 1 1
. . . x |  2 |  *  *  * 30 |  0  0  1  0  1 1 | 0 1 1 1
--------+----+-------------+------------------+--------
x3x . . |  6 |  3  3  0  0 | 10  *  *  *  * * | 1 1 0 0
x . x . |  4 |  2  0  2  0 |  * 15  *  *  * * | 1 0 1 0
x . . x |  4 |  2  0  0  2 |  *  * 15  *  * * | 0 1 1 0
. x x . |  4 |  0  2  2  0 |  *  *  * 15  * * | 1 0 0 1
. x . x |  4 |  0  2  0  2 |  *  *  *  * 15 * | 0 1 0 1
. . x5x | 10 |  0  0  5  5 |  *  *  *  *  * 6 | 0 0 1 1
--------+----+-------------+------------------+--------
x3x x . ♦ 12 |  6  6  6  0 |  2  3  0  3  0 0 | 5 * * *
x3x . x ♦ 12 |  6  6  0  6 |  2  0  3  0  3 0 | * 5 * *
x . x5x ♦ 20 | 10  0 10 10 |  0  5  5  0  0 2 | * * 3 *
. x x5x ♦ 20 |  0 10 10 10 |  0  0  0  5  5 2 | * * * 3


xux xxx10ooo&#xt   → both heights = sqrt(3)/2 = 0.866025
(dip || pseudo (x,u)-dip || dip)

o.. o..10o..     | 20  *  * |  1  2  1  0  0  0  0 |  2 1  2  1 0  0  0 0 | 1 1  2 0 0
.o. .o.10.o.     |  * 20  * |  0  0  1  2  1  0  0 |  0 0  2  1 1  2  0 0 | 0 1  2 1 0
..o ..o10..o     |  *  * 20 |  0  0  0  0  1  1  2 |  0 0  0  1 0  2  2 1 | 0 0  2 1 1
-----------------+----------+----------------------+----------------------+-----------
x.. ...  ...     |  2  0  0 | 10  *  *  *  *  *  * |  2 0  0  1 0  0  0 0 | 1 0  2 0 0
... x..  ...     |  2  0  0 |  * 20  *  *  *  *  * |  1 1  1  0 0  0  0 0 | 1 1  1 0 0
oo. oo.10oo.&#x  |  1  1  0 |  *  * 20  *  *  *  * |  0 0  2  1 0  0  0 0 | 0 1  2 0 0
... .x.  ...     |  0  2  0 |  *  *  * 20  *  *  * |  0 0  1  0 1  1  0 0 | 0 1  1 1 0
.oo .oo10.oo&#x  |  0  1  1 |  *  *  *  * 20  *  * |  0 0  0  1 0  2  0 0 | 0 0  2 1 0
..x ...  ...     |  0  0  2 |  *  *  *  *  * 10  * |  0 0  0  1 0  0  2 0 | 0 0  2 0 1
... ..x  ...     |  0  0  2 |  *  *  *  *  *  * 20 |  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 | 10 *  *  * *  *  * * | 1 0  1 0 0
... x..10o..     | 10  0  0 |  0 10  0  0  0  0  0 |  * 2  *  * *  *  * * | 1 1  0 0 0
... xx.  ...&#x  |  2  2  0 |  0  1  2  1  0  0  0 |  * * 20  * *  *  * * | 0 1  1 0 0
xux ...  ...&#xt |  2  2  2 |  1  0  2  0  2  1  0 |  * *  * 10 *  *  * * | 0 0  2 0 0
... .x.10.o.     |  0 10  0 |  0  0  0 10  0  0  0 |  * *  *  * 2  *  * * | 0 1  0 1 0
... .xx  ...&#x  |  0  2  2 |  0  0  0  1  2  0  1 |  * *  *  * * 20  * * | 0 0  1 1 0
..x ..x  ...     |  0  0  4 |  0  0  0  0  0  2  2 |  * *  *  * *  * 10 * | 0 0  1 0 1
... ..x10..o     |  0  0 10 |  0  0  0  0  0  0 10 |  * *  *  * *  *  * 2 | 0 0  0 1 1
-----------------+----------+----------------------+----------------------+-----------
x.. x..10o..     ♦ 20  0  0 | 10 20  0  0  0  0  0 | 10 2  0  0 0  0  0 0 | 1 *  * * *
... xx.10oo.&#x  ♦ 10 10  0 |  0 10 10 10  0  0  0 |  0 1 10  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 | * * 10 * *
... .xx10.oo&#x  ♦  0 10 10 |  0  0  0 10 10  0 10 |  0 0  0  0 1 10  0 1 | * *  * 2 *
..x ..x10..o     ♦  0  0 20 |  0  0  0  0  0 10 20 |  0 0  0  0 0  0 10 2 | * *  * * 1

or
o.. o..10o..      & | 40  * |  1  2  1  0 |  2 1  2  1 0 | 1 1  2
.o. .o.10.o.        |  * 20 |  0  0  2  2 |  0 0  4  1 1 | 0 2  2
--------------------+-------+-------------+--------------+-------
x.. ...  ...      & |  2  0 | 20  *  *  * |  2 0  0  1 0 | 1 0  2
... x..  ...      & |  2  0 |  * 40  *  * |  1 1  1  0 0 | 1 1  1
oo. oo.10oo.&#x   & |  1  1 |  *  * 40  * |  0 0  2  1 0 | 0 1  2
... .x.  ...        |  0  2 |  *  *  * 20 |  0 0  2  0 1 | 0 2  1
--------------------+-------+-------------+--------------+-------
x.. x..  ...      & |  4  0 |  2  2  0  0 | 20 *  *  * * | 1 0  1
... x..10o..      & | 10  0 |  0 10  0  0 |  * 4  *  * * | 1 1  0
... xx.  ...&#x   & |  2  2 |  0  1  2  1 |  * * 40  * * | 0 1  1
xux ...  ...&#xt    |  4  2 |  2  0  4  0 |  * *  * 10 * | 0 0  2
... .x.10.o.        |  0 10 |  0  0  0 10 |  * *  *  * 2 | 0 2  0
--------------------+-------+-------------+--------------+-------
x.. x..10o..      & ♦ 20  0 | 10 20  0  0 | 10 2  0  0 0 | 2 *  *
... xx.10oo.&#x   & ♦ 10 10 |  0 10 10 10 |  0 1 10  0 1 | * 4  *
xux xxx  ...&#xt    ♦  8  4 |  4  4  8  2 |  2 0  4  2 0 | * * 10


xux xxx5xxx&#xt   → both heights = sqrt(3)/2 = 0.866025
(dip || pseudo (x,u)-dip || dip)

o.. o..5o..     | 20  *  * |  1  1  1  1  0  0  0  0  0  0 | 1 1 1  1  1  1 0  0  0 0 0 0 | 1 1 1 1 0 0
.o. .o.5.o.     |  * 20  * |  0  0  0  1  1  1  1  0  0  0 | 0 0 0  1  1  1 1  1  1 0 0 0 | 0 1 1 1 1 0
..o ..o5..o     |  *  * 20 |  0  0  0  0  0  0  1  1  1  1 | 0 0 0  1  0  0 0  1  1 1 1 1 | 0 1 1 0 1 1
----------------+----------+-------------------------------+------------------------------+------------
x.. ... ...     |  2  0  0 | 10  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0 0  0  0 0 0 0 | 1 1 1 0 0 0
... x.. ...     |  2  0  0 |  * 10  *  *  *  *  *  *  *  * | 1 0 1  0  1  0 0  0  0 0 0 0 | 1 1 0 1 0 0
... ... x..     |  2  0  0 |  *  * 10  *  *  *  *  *  *  * | 0 1 1  0  0  1 0  0  0 0 0 0 | 1 0 1 1 0 0
oo. oo.5oo.&#x  |  1  1  0 |  *  *  * 20  *  *  *  *  *  * | 0 0 0  1  1  1 0  0  0 0 0 0 | 0 1 1 1 0 0
... .x. ...     |  0  2  0 |  *  *  *  * 10  *  *  *  *  * | 0 0 0  0  1  0 1  1  0 0 0 0 | 0 1 0 1 1 0
... ... .x.     |  0  2  0 |  *  *  *  *  * 10  *  *  *  * | 0 0 0  0  0  1 1  0  1 0 0 0 | 0 0 1 1 1 0
.oo .oo5.oo&#x  |  0  1  1 |  *  *  *  *  *  * 20  *  *  * | 0 0 0  1  0  0 0  1  1 0 0 0 | 0 1 1 0 1 0
..x ... ...     |  0  0  2 |  *  *  *  *  *  *  * 10  *  * | 0 0 0  1  0  0 0  0  0 1 1 0 | 0 1 1 0 0 1
... ..x ...     |  0  0  2 |  *  *  *  *  *  *  *  * 10  * | 0 0 0  0  0  0 0  1  0 1 0 1 | 0 1 0 0 1 1
... ... ..x     |  0  0  2 |  *  *  *  *  *  *  *  *  * 10 | 0 0 0  0  0  0 0  0  1 0 1 1 | 0 0 1 0 1 1
----------------+----------+-------------------------------+------------------------------+------------
x.. x.. ...     |  4  0  0 |  2  2  0  0  0  0  0  0  0  0 | 5 * *  *  *  * *  *  * * * * | 1 1 0 0 0 0
x.. ... x..     |  4  0  0 |  2  0  2  0  0  0  0  0  0  0 | * 5 *  *  *  * *  *  * * * * | 1 0 1 0 0 0
... x..5x..     | 10  0  0 |  0  5  5  0  0  0  0  0  0  0 | * * 2  *  *  * *  *  * * * * | 1 0 0 1 0 0
xux ... ...&#xt |  2  2  2 |  1  0  0  2  0  0  2  1  0  0 | * * * 10  *  * *  *  * * * * | 0 1 1 0 0 0
... xx. ...&#x  |  2  2  0 |  0  1  0  2  1  0  0  0  0  0 | * * *  * 10  * *  *  * * * * | 0 1 0 1 0 0
... ... xx.&#x  |  2  2  0 |  0  0  1  2  0  1  0  0  0  0 | * * *  *  * 10 *  *  * * * * | 0 0 1 1 0 0
... .x.5.x.     |  0 10  0 |  0  0  0  0  5  5  0  0  0  0 | * * *  *  *  * 2  *  * * * * | 0 0 0 1 1 0
... .xx ...&#x  |  0  2  2 |  0  0  0  0  1  0  2  0  1  0 | * * *  *  *  * * 10  * * * * | 0 1 0 0 1 0
... ... .xx&#x  |  0  2  2 |  0  0  0  0  0  1  2  0  0  1 | * * *  *  *  * *  * 10 * * * | 0 0 1 0 1 0
..x ..x ...     |  0  0  4 |  0  0  0  0  0  0  0  2  2  0 | * * *  *  *  * *  *  * 5 * * | 0 1 0 0 0 1
..x ... ..x     |  0  0  4 |  0  0  0  0  0  0  0  2  0  2 | * * *  *  *  * *  *  * * 5 * | 0 0 1 0 0 1
... ..x5..x     |  0  0 10 |  0  0  0  0  0  0  0  0  5  5 | * * *  *  *  * *  *  * * * 2 | 0 0 0 0 1 1
----------------+----------+-------------------------------+------------------------------+------------
x.. x..5x..     ♦ 20  0  0 | 10 10 10  0  0  0  0  0  0  0 | 5 5 2  0  0  0 0  0  0 0 0 0 | 1 * * * * *
xux xxx ...&#xt ♦  4  4  4 |  2  2  0  4  2  0  4  2  2  0 | 1 0 0  2  2  0 0  2  0 1 0 0 | * 5 * * * *
xux ... xxx&#xt ♦  4  4  4 |  2  0  2  4  0  2  4  2  0  2 | 0 1 0  2  0  2 0  0  2 0 1 0 | * * 5 * * *
... xx.5xx.&#x  ♦ 10 10  0 |  0  5  5 10  5  5  0  0  0  0 | 0 0 1  0  5  5 1  0  0 0 0 0 | * * * 2 * *
... .xx5.xx&#x  ♦  0 10 10 |  0  0  0  0  5  5 10  0  5  5 | 0 0 0  0  0  0 1  5  5 0 0 1 | * * * * 2 *
..x ..x5..x     ♦  0  0 20 |  0  0  0  0  0  0  0 10 10 10 | 0 0 0  0  0  0 0  0  0 5 5 2 | * * * * * 1

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