Acronym tisdip, K-4.18 Name triangle - square duoprism,square - cube wedge ` ©` Circumradius sqrt(5/6) = 0.912871 General of army (is itself convex) Colonel of regiment (is itself locally convex) Confer general duoprisms: n,m-dip   2n,m-dip   3,n-dip   4,n-dip 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
```