Acronym tisdip, K-4.18 Name triangle - square duoprism,square - cube wedge,vertex figure of nit |,>,O device line pyramid prism prism = |>|| ` © ©` Circumradius sqrt(5/6) = 0.912871 Coordinates (1/2, 1/2, 1/2, 1/sqrt(12))             & all changes of sign in first 3 coords. (cube face) (1/2, 1/2, 0, -1/sqrt(3))       & all changes of sign in 1st & 2nd coord. (opposite square) Volume sqrt(3)/4 = 0.433013 General of army (is itself convex) Colonel of regiment (is itself locally convex) Dihedral angles at {4} between cube and trip:   90° at {3} between trip and trip:   90° at {4} between cube and cube:   60° Confer general duoprisms: n,m-dip   2n,m-dip   3,n-dip   4,n-dip   general polytopal classes: segmentochora   bistratic lace towers   lace simplices Externallinks

Incidence matrix according to Dynkin symbol

```x3o x4o

. . . . | 12 ♦  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 12  * | 1  2 0 | 2 1
. . x . |  2 |  * 12 | 0  2 1 | 1 2
--------+----+-------+--------+----
x3o . . |  3 |  3  0 | 4  * * | 2 0
x . x . |  4 |  2  2 | * 12 * | 1 1
. . x4o |  4 |  0  4 | *  * 3 | 0 2
--------+----+-------+--------+----
x3o x . ♦  6 |  6  3 | 2  3 0 | 4 *
x . x4o ♦  8 |  4  8 | 0  4 2 | * 3
```

```x x x3o

. . . . | 12 ♦ 1 1  2 | 1 2 2 1 | 2 1 1
--------+----+--------+---------+------
x . . . |  2 | 6 *  * | 1 2 0 0 | 2 1 0
. x . . |  2 | * 6  * | 1 0 2 0 | 2 0 1
. . x . |  2 | * * 12 | 0 1 1 1 | 1 1 1
--------+----+--------+---------+------
x x . . |  4 | 2 2  0 | 3 * * * | 2 0 0
x . x . |  4 | 2 0  2 | * 6 * * | 1 1 0
. x x . |  4 | 0 2  2 | * * 6 * | 1 0 1
. . x3o |  3 | 0 0  3 | * * * 4 | 0 1 1
--------+----+--------+---------+------
x x x . ♦  8 | 4 4  4 | 2 2 2 0 | 3 * *
x . x3o ♦  6 | 3 0  6 | 0 3 0 2 | * 2 *
. x x3o ♦  6 | 0 3  6 | 0 0 3 2 | * * 2
```

```x3o x4/3o

. . .   . | 12 ♦  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 12  * | 1  2 0 | 2 1
. . x   . |  2 |  * 12 | 0  2 1 | 1 2
----------+----+-------+--------+----
x3o .   . |  3 |  3  0 | 4  * * | 2 0
x . x   . |  4 |  2  2 | * 12 * | 1 1
. . x4/3o |  4 |  0  4 | *  * 3 | 0 2
----------+----+-------+--------+----
x3o x   . ♦  6 |  6  3 | 2  3 0 | 4 *
x . x4/3o ♦  8 |  4  8 | 0  4 2 | * 3
```

```x3/2o x4o

.   . . . | 12 ♦  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x   . . . |  2 | 12  * | 1  2 0 | 2 1
.   . x . |  2 |  * 12 | 0  2 1 | 1 2
----------+----+-------+--------+----
x3/2o . . |  3 |  3  0 | 4  * * | 2 0
x   . x . |  4 |  2  2 | * 12 * | 1 1
.   . x4o |  4 |  0  4 | *  * 3 | 0 2
----------+----+-------+--------+----
x3/2o x . ♦  6 |  6  3 | 2  3 0 | 4 *
x   . x4o ♦  8 |  4  8 | 0  4 2 | * 3
```

```x3/2o x4/3o

.   . .   . | 12 ♦  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 12  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 12 | 0  2 1 | 1 2
------------+----+-------+--------+----
x3/2o .   . |  3 |  3  0 | 4  * * | 2 0
x   . x   . |  4 |  2  2 | * 12 * | 1 1
.   . x4/3o |  4 |  0  4 | *  * 3 | 0 2
------------+----+-------+--------+----
x3/2o x   . ♦  6 |  6  3 | 2  3 0 | 4 *
x   . x4/3o ♦  8 |  4  8 | 0  4 2 | * 3
```

```x4o s3s

. . demi( . . ) | 12 ♦  2  2 | 1 1  4 | 2 2
----------------+----+-------+--------+----
x . demi( . . ) |  2 | 12  * | 1 0  2 | 1 2
. . sefa( s3s ) |  2 |  * 12 | 0 1  2 | 2 1
----------------+----+-------+--------+----
x4o demi( . . ) |  4 |  4  0 | 3 *  * | 0 2
. .       s3s   ♦  3 |  0  3 | * 4  * | 2 0
x . sefa( s3s ) |  4 |  2  2 | * * 12 | 1 1
----------------+----+-------+--------+----
x .       s3s   ♦  6 |  3  6 | 0 2  3 | 4 *
x4o sefa( s3s ) ♦  8 |  8  4 | 2 0  4 | * 3
```

```x x s3s

. . demi( . . ) | 12 ♦ 1 1  2 | 1 1 2 2 | 1 1 2
----------------+----+--------+---------+------
x . demi( . . ) |  2 | 6 *  * | 0 1 2 0 | 1 0 2
. x demi( . . ) |  2 | * 6  * | 0 1 0 2 | 0 1 2
. . sefa( s3s ) |  2 | * * 12 | 1 0 1 1 | 1 1 1
----------------+----+--------+---------+------
. .       s3s   ♦  3 | 0 0  3 | 4 * * * | 1 1 0
x x demi( . . ) |  4 | 2 2  0 | * 3 * * | 0 0 2
x . sefa( s3s ) |  4 | 2 0  2 | * * 6 * | 1 0 1
. x sefa( s3s ) |  4 | 0 2  2 | * * * 6 | 0 1 1
----------------+----+--------+---------+------
x .       s3s   ♦  6 | 3 0  6 | 2 0 3 0 | 2 * *
. x       s3s   ♦  6 | 0 3  6 | 2 0 0 3 | * 2 *
x x sefa( s3s ) ♦  8 | 4 4  4 | 0 2 2 2 | * * 3
```

```xx xx3oo&#x   → height = 1
(trip || trip)

o. o.3o.    | 6 * ♦ 1 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.o .o3.o    | * 6 ♦ 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
------------+-----+-----------+-------------+--------
x. .. ..    | 2 0 | 3 * * * * | 2 0 1 0 0 0 | 1 2 0 0
.. x. ..    | 2 0 | * 6 * * * | 1 1 0 1 0 0 | 1 1 1 0
oo oo3oo&#x | 1 1 | * * 6 * * | 0 0 1 2 0 0 | 0 2 1 0
.x .. ..    | 0 2 | * * * 3 * | 0 0 1 0 2 0 | 0 2 0 1
.. .x ..    | 0 2 | * * * * 6 | 0 0 0 1 1 1 | 0 1 1 1
------------+-----+-----------+-------------+--------
x. x. ..    | 4 0 | 2 2 0 0 0 | 3 * * * * * | 1 1 0 0
.. x.3o.    | 3 0 | 0 3 0 0 0 | * 2 * * * * | 1 0 1 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * 3 * * * | 0 2 0 0
.. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * 6 * * | 0 1 1 0
.x .x ..    | 0 4 | 0 0 0 2 2 | * * * * 3 * | 0 1 0 1
.. .x3.o    | 0 3 | 0 0 0 0 3 | * * * * * 2 | 0 0 1 1
------------+-----+-----------+-------------+--------
x. x.3o.    ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 | 1 * * *
xx xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 1 0 2 2 1 0 | * 3 * *
.. xx3oo&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 3 0 1 | * * 2 *
.x .x3.o    ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 3 2 | * * * 1
```

```ox xx4oo&#x   → height = sqrt(3)/2 = 0.866025
({4} || cube)

o. o.4o.    | 4 * ♦ 2 2 0 0 | 1 1 4 0 0 | 2 2 0
.o .o4.o    | * 8 ♦ 0 1 1 2 | 0 1 2 2 1 | 2 1 1
------------+-----+---------+-----------+------
.. x. ..    | 2 0 | 4 * * * | 1 0 2 0 0 | 1 2 0
oo oo4oo&#x | 1 1 | * 8 * * | 0 1 2 0 0 | 2 1 0
.x .. ..    | 0 2 | * * 4 * | 0 1 0 2 0 | 2 0 1
.. .x ..    | 0 2 | * * * 8 | 0 0 1 1 1 | 1 1 1
------------+-----+---------+-----------+------
.. x.4o.    | 4 0 | 4 0 0 0 | 1 * * * * | 0 2 0
ox .. ..&#x | 1 2 | 0 2 1 0 | * 4 * * * | 2 0 0
.. xx ..&#x | 2 2 | 1 2 0 1 | * * 8 * * | 1 1 0
.x .x ..    | 0 4 | 0 0 2 2 | * * * 4 * | 1 0 1
.. .x4.o    | 0 4 | 0 0 0 4 | * * * * 2 | 0 1 1
------------+-----+---------+-----------+------
ox xx ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | 4 * *
.. xx4oo&#x ♦ 4 4 | 4 4 0 4 | 1 0 4 0 1 | * 2 *
.x .x4.o    ♦ 0 8 | 0 0 4 8 | 0 0 0 4 2 | * * 1
```

```ox xx xx&#x   → height = sqrt(3)/2 = 0.866025
({4} || cube)

o. o. o.    | 4 * ♦ 1 1 2 0 0 0 | 1 1 2 2 0 0 0 | 1 1 2 0
.o .o .o    | * 8 ♦ 0 0 1 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
------------+-----+-------------+---------------+--------
.. x. ..    | 2 0 | 2 * * * * * | 1 0 2 0 0 0 0 | 1 0 2 0
.. .. x.    | 2 0 | * 2 * * * * | 1 0 0 2 0 0 0 | 0 1 2 0
oo oo oo&#x | 1 1 | * * 8 * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.x .. ..    | 0 2 | * * * 4 * * | 0 1 0 0 1 1 0 | 1 1 0 1
.. .x ..    | 0 2 | * * * * 4 * | 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x    | 0 2 | * * * * * 4 | 0 0 0 1 0 1 1 | 0 1 1 1
------------+-----+-------------+---------------+--------
.. x. x.    | 4 0 | 2 2 0 0 0 0 | 1 * * * * * * | 0 0 2 0
ox .. ..&#x | 1 2 | 0 0 2 1 0 0 | * 4 * * * * * | 1 1 0 0
.. xx ..&#x | 2 2 | 1 0 2 0 1 0 | * * 4 * * * * | 1 0 1 0
.. .. xx&#x | 2 2 | 0 1 2 0 0 1 | * * * 4 * * * | 0 1 1 0
.x .x ..    | 0 4 | 0 0 0 2 2 0 | * * * * 2 * * | 1 0 0 1
.x .. .x    | 0 4 | 0 0 0 2 0 2 | * * * * * 2 * | 0 1 0 1
.. .x .x    | 0 4 | 0 0 0 0 2 2 | * * * * * * 2 | 0 0 1 1
------------+-----+-------------+---------------+--------
ox xx ..&#x ♦ 2 4 | 1 0 4 2 2 0 | 0 2 2 0 1 0 0 | 2 * * *
ox .. xx&#x ♦ 2 4 | 1 0 4 2 0 2 | 0 2 0 2 0 1 0 | * 2 * *
.. xx xx&#x ♦ 4 4 | 2 2 4 0 2 2 | 1 0 2 2 0 0 1 | * * 2 *
.x .x .x    ♦ 0 8 | 0 0 0 4 4 4 | 0 0 0 0 2 2 2 | * * * 1
```

```xxx3ooo oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
({3} || pseudo q x3o || {3})

o..3o.. o..     | 3 * * | 2 2 0 0 0 | 1 4 1 0 0 0 | 2 2 0
.o.3.o. .o.     | * 6 * | 0 1 2 1 0 | 0 2 1 1 2 0 | 1 2 1
..o3..o ..o     | * * 3 | 0 0 0 2 2 | 0 0 1 0 4 1 | 0 2 2
----------------+-------+-----------+-------------+------
x.. ... ...     | 2 0 0 | 3 * * * * | 1 2 0 0 0 0 | 2 1 0
oo.3oo. oo.&#x  | 1 1 0 | * 6 * * * | 0 2 1 0 0 0 | 1 2 0
.x. ... ...     | 0 2 0 | * * 6 * * | 0 1 0 1 1 0 | 1 1 1
.oo3.oo .oo&#x  | 0 1 1 | * * * 6 * | 0 0 1 0 2 0 | 0 2 1
..x ... ...     | 0 0 2 | * * * * 3 | 0 0 0 0 2 1 | 0 1 2
----------------+-------+-----------+-------------+------
x..3o.. ...     | 3 0 0 | 3 0 0 0 0 | 1 * * * * * | 2 0 0
xx. ... ...&#x  | 2 2 0 | 1 2 1 0 0 | * 6 * * * * | 1 1 0
... ... oqo&#xt | 1 2 1 | 0 2 0 2 0 | * * 3 * * * | 0 2 0
.x.3.o. ...     | 0 3 0 | 0 0 3 0 0 | * * * 2 * * | 1 0 1
.xx ... ...&#x  | 0 2 2 | 0 0 1 2 1 | * * * * 6 * | 0 1 1
..x3..o ...     | 0 0 3 | 0 0 0 0 3 | * * * * * 1 | 0 0 2
----------------+-------+-----------+-------------+------
xx.3oo. ...&#x  ♦ 3 3 0 | 3 3 3 0 0 | 1 3 0 1 0 0 | 2 * *
xxx ... oqo&#xt ♦ 2 4 2 | 1 4 2 4 1 | 0 2 2 0 2 0 | * 3 *
.xx3.oo ...&#x  ♦ 0 3 3 | 0 0 3 3 3 | 0 0 0 1 3 1 | * * 2
```
```or
o..3o.. o..     & | 6 * | 2  2 0 | 1  4 1 0 | 2 2
.o.3.o. .o.       | * 6 | 0  2 2 | 0  4 1 1 | 2 2
------------------+-----+--------+----------+----
x.. ... ...     & | 2 0 | 6  * * | 1  2 0 0 | 2 1
oo.3oo. oo.&#x  & | 1 1 | * 12 * | 0  2 1 0 | 1 2
.x. ... ...       | 0 2 | *  * 6 | 0  2 0 1 | 2 1
------------------+-----+--------+----------+----
x..3o.. ...     & | 3 0 | 3  0 0 | 2  * * * | 2 0
xx. ... ...&#x  & | 2 2 | 1  2 1 | * 12 * * | 1 1
... ... oqo&#xt   | 2 2 | 0  4 0 | *  * 3 * | 0 2
.x.3.o. ...       | 0 3 | 0  0 3 | *  * * 2 | 2 0
------------------+-----+--------+----------+----
xx.3oo. ...&#x  & ♦ 3 3 | 3  3 3 | 1  3 0 1 | 4 *
xxx ... oqo&#xt   ♦ 4 4 | 2  8 2 | 0  4 2 0 | * 3
```

```xxx xxx&#x   →  all lacing heights = 1

o.. o..    | 4 * * | 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.o. .o.    | * 4 * | 0 0 1 0 1 1 1 0 0 | 0 1 1 0 0 1 1 1 1 0 | 1 0 1 1 1
..o ..o    | * * 4 | 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1
-----------+-------+-------------------+---------------------+----------
x.. ...    | 2 0 0 | 2 * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
... x..    | 2 0 0 | * 2 * * * * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
oo. oo.&#x | 1 1 0 | * * 4 * * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
o.o o.o&#x | 1 0 0 | * * * 4 * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.x. ...    | 0 2 0 | * * * * 2 * * * * | 0 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0 2 0 | * * * * * 2 * * * | 0 0 1 0 0 0 1 0 1 0 | 1 0 0 1 1
.oo .oo&#x | 0 1 1 | * * * * * * 4 * * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
..x ...    | 0 0 2 | * * * * * * * 2 * | 0 0 0 1 0 0 0 1 0 1 | 0 1 1 0 1
... ..x    | 0 0 2 | * * * * * * * * 2 | 0 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1
-----------+-------+-------------------+---------------------+----------
x.. x..    | 4 0 0 | 2 2 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
xx. ...&#x | 2 2 0 | 1 0 2 0 1 0 0 0 0 | * 2 * * * * * * * * | 1 0 1 0 0
... xx.&#x | 2 2 0 | 0 1 2 0 0 1 0 0 0 | * * 2 * * * * * * * | 1 0 0 1 0
x.x ...&#x | 2 0 2 | 1 0 0 2 0 0 0 1 0 | * * * 2 * * * * * * | 0 1 1 0 0
... x.x&#x | 2 0 2 | 0 1 0 2 0 0 0 0 1 | * * * * 2 * * * * * | 0 1 0 1 0
ooo ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 0 | * * * * * 4 * * * * | 0 0 1 1 0
.x. .x.    | 0 4 0 | 0 0 0 0 2 2 0 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0 2 2 | 0 0 0 0 1 0 2 1 0 | * * * * * * * 2 * * | 0 0 1 0 1
... .xx&#x | 0 2 2 | 0 0 0 0 0 1 2 0 1 | * * * * * * * * 2 * | 0 0 0 1 1
..x ..x    | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-------------------+---------------------+----------
xx. xx.&#x ♦ 4 4 0 | 2 2 4 0 2 2 0 0 0 | 1 2 2 0 0 0 1 0 0 0 | 1 * * * *
x.x x.x&#x ♦ 4 0 4 | 2 2 0 4 0 0 0 2 2 | 1 0 0 2 2 0 0 0 0 1 | * 1 * * *
xxx ...&#x ♦ 2 2 2 | 1 0 2 2 1 0 2 1 0 | 0 1 0 1 0 2 0 1 0 0 | * * 2 * *
... xxx&#x ♦ 2 2 2 | 0 1 2 2 0 1 2 0 1 | 0 0 1 0 1 2 0 0 1 0 | * * * 2 *
.xx .xx&#x ♦ 0 4 4 | 0 0 0 0 2 2 4 2 2 | 0 0 0 0 0 0 1 2 2 1 | * * * * 1
```