Acronym	squadedip, K-4.97
Name	square - decagon duoprism
Circumradius	sqrt[(4+sqrt(5))/2] = 1.765796
Volume	5 sqrt[5+2 sqrt(5)]/2 = 7.694209
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	at {4} between cube and cube:   144° at {4} between cube and dip:   90° at {10} between dip and dip:   90°
Face vector	40, 80, 54, 14
Confer	general duoprisms: n,m-dip   2n,m-dip   2n,2m-dip   4,n-dip   4,2n-dip   10,n-dip   general polytopal classes: segmentochora   bistratic lace towers
External links

Incidence matrix according to Dynkin symbol

x4o x10o

. . .  . | 40 |  2  2 |  1  4 1 |  2 2
---------+----+-------+---------+-----
x . .  . |  2 | 40  * |  1  2 0 |  2 1
. . x  . |  2 |  * 40 |  0  2 1 |  1 2
---------+----+-------+---------+-----
x4o .  . |  4 |  4  0 | 10  * * |  2 0
x . x  . |  4 |  2  2 |  * 40 * |  1 1
. . x10o | 10 |  0 10 |  *  * 4 |  0 2
---------+----+-------+---------+-----
x4o x  . ♦  8 |  8  4 |  2  4 0 | 10 *
x . x10o ♦ 20 | 10 20 |  0 10 2 |  * 4

x4o x10/9o

. . .    . | 40 |  2  2 |  1  4 1 |  2 2
-----------+----+-------+---------+-----
x . .    . |  2 | 40  * |  1  2 0 |  2 1
. . x    . |  2 |  * 40 |  0  2 1 |  1 2
-----------+----+-------+---------+-----
x4o .    . |  4 |  4  0 | 10  * * |  2 0
x . x    . |  4 |  2  2 |  * 40 * |  1 1
. . x10/9o | 10 |  0 10 |  *  * 4 |  0 2
-----------+----+-------+---------+-----
x4o x    . ♦  8 |  8  4 |  2  4 0 | 10 *
x . x10/9o ♦ 20 | 10 20 |  0 10 2 |  * 4

x4/3o x10o

.   . .  . | 40 |  2  2 |  1  4 1 |  2 2
-----------+----+-------+---------+-----
x   . .  . |  2 | 40  * |  1  2 0 |  2 1
.   . x  . |  2 |  * 40 |  0  2 1 |  1 2
-----------+----+-------+---------+-----
x4/3o .  . |  4 |  4  0 | 10  * * |  2 0
x   . x  . |  4 |  2  2 |  * 40 * |  1 1
.   . x10o | 10 |  0 10 |  *  * 4 |  0 2
-----------+----+-------+---------+-----
x4/3o x  . ♦  8 |  8  4 |  2  4 0 | 10 *
x   . x10o ♦ 20 | 10 20 |  0 10 2 |  * 4

x4/3o x10/9o

.   . .    . | 40 |  2  2 |  1  4 1 |  2 2
-------------+----+-------+---------+-----
x   . .    . |  2 | 40  * |  1  2 0 |  2 1
.   . x    . |  2 |  * 40 |  0  2 1 |  1 2
-------------+----+-------+---------+-----
x4/3o .    . |  4 |  4  0 | 10  * * |  2 0
x   . x    . |  4 |  2  2 |  * 40 * |  1 1
.   . x10/9o | 10 |  0 10 |  *  * 4 |  0 2
-------------+----+-------+---------+-----
x4/3o x    . ♦  8 |  8  4 |  2  4 0 | 10 *
x   . x10/9o ♦ 20 | 10 20 |  0 10 2 |  * 4

x x x10o

. . .  . | 40 |  1  1  2 |  1  2  2 1 |  2 1 1
---------+----+----------+------------+-------
x . .  . |  2 | 20  *  * |  1  2  0 0 |  2 1 0
. x .  . |  2 |  * 20  * |  1  0  2 0 |  2 0 1
. . x  . |  2 |  *  * 40 |  0  1  1 1 |  1 1 1
---------+----+----------+------------+-------
x x .  . |  4 |  2  2  0 | 10  *  * * |  2 0 0
x . x  . |  4 |  2  0  2 |  * 20  * * |  1 1 0
. x x  . |  4 |  0  2  2 |  *  * 20 * |  1 0 1
. . x10o | 10 |  0  0 10 |  *  *  * 4 |  0 1 1
---------+----+----------+------------+-------
x x x  . ♦  8 |  4  4  4 |  2  2  2 0 | 10 * *
x . x10o ♦ 20 | 10  0 20 |  0 10  0 2 |  * 2 *
. x x10o ♦ 20 |  0 10 20 |  0  0 10 2 |  * * 2

x4o x5x

. . . . | 40 |  2  1  1 |  1  2  2 1 | 1 1 2
--------+----+----------+------------+------
x . . . |  2 | 40  *  * |  1  1  1 0 | 1 1 1
. . x . |  2 |  * 20  * |  0  2  0 1 | 1 0 2
. . . x |  2 |  *  * 20 |  0  0  2 1 | 0 1 2
--------+----+----------+------------+------
x4o . . |  4 |  4  0  0 | 10  *  * * | 1 1 0
x . x . |  4 |  2  2  0 |  * 20  * * | 1 0 1
x . . x |  4 |  2  0  2 |  *  * 20 * | 0 1 1
. . x5x | 10 |  0  5  5 |  *  *  * 4 | 0 0 2
--------+----+----------+------------+------
x4o x . ♦  8 |  8  4  0 |  2  4  0 0 | 5 * *
x4o . x ♦  8 |  8  0  4 |  2  0  4 0 | * 5 *
x . x5x ♦ 20 | 10 10 10 |  0  5  5 2 | * * 4

x x x5x

. . . . | 40 |  1  1  1  1 |  1  1  1  1  1 1 | 1 1 1 1
--------+----+-------------+------------------+--------
x . . . |  2 | 20  *  *  * |  1  1  1  0  0 0 | 1 1 1 0
. x . . |  2 |  * 20  *  * |  1  0  0  1  1 0 | 1 1 0 1
. . x . |  2 |  *  * 20  * |  0  1  0  1  0 1 | 1 0 1 1
. . . x |  2 |  *  *  * 20 |  0  0  1  0  1 1 | 0 1 1 1
--------+----+-------------+------------------+--------
x x . . |  4 |  2  2  0  0 | 10  *  *  *  * * | 1 1 0 0
x . x . |  4 |  2  0  2  0 |  * 10  *  *  * * | 1 0 1 0
x . . x |  4 |  2  0  0  2 |  *  * 10  *  * * | 0 1 1 0
. x x . |  4 |  0  2  2  0 |  *  *  * 10  * * | 1 0 0 1
. x . x |  4 |  0  2  0  2 |  *  *  *  * 10 * | 0 1 0 1
. . x5x | 10 |  0  0  5  5 |  *  *  *  *  * 4 | 0 0 1 1
--------+----+-------------+------------------+--------
x x x . ♦  8 |  4  4  4  0 |  2  2  0  2  0 0 | 5 * * *
x x . x ♦  8 |  4  4  0  4 |  2  0  2  0  2 0 | * 5 * *
x . x5x ♦ 20 | 10  0 10 10 |  0  5  5  0  0 2 | * * 2 *
. x x5x ♦ 20 |  0 10 10 10 |  0  0  0  5  5 2 | * * * 2

xxx10ooo oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
({10} || pseudo (x,q)-dip || {10})

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

xxx5xxx oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
({10} || pseudo (x,x,q)-dip || {10})

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