﻿ tedhin
Acronym tedhin
square || hex
Circumradius sqrt(5/8) = 0.790569
Lace city
in approx. ASCII-art
```    4

t       T   -- alt. hex

\
+-- bidrap
wobei
4 =  x x     (square) = bidimin. of (oct = bidimin. gyro hex)
t = xo ox&#x (tet)
T = ox xo&#x (dual tet)
```
Lace hyper city
in approx. ASCII-art
 ``` x x ``` ```x o o x o x x o ```
({4} || alternate hex)
Coordinates
1. (1/sqrt(2), 0, 0, 0, 1/sqrt(8))   & all permutations and changes of sign in the first 2 coordinates only
(top square)
2. (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), -1/sqrt(8))   & any even change of signs in the first 4 coordinates only
(bottom hex)
Confer
uniform relative:
hin
segmentotera:
dihin   bidhin   squasquasc   rappy
general polytopal classes:
segmentotera

The hemipenteract (hin) could be given as hex || gyro hex. Here the top-hex (itself being a tegum sum of 2 perp. squares) has to be tetradiminished at all vertices of one of its diametral squares. Simultanuously the bottom-hex only gets marginally rasped at 4 tets. The sefa clearly is related to the vertex figure of hin, i.e. rap. In fact, as those will intersect here, these become bidraps In other words, one chops off 4 (intersecting) rappies.

Incidence matrix according to Dynkin symbol

```xoo oxo xox oxx&#x   → height(1,2) = 0
height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107
(hex || part. para square)

o.. o.. o.. o..    & | 8 * | 1 1  4  2 0 |  6  6 2 2 1  4 0 | 2 4 2 1 1  6  6 | 1 2 4 2
..o ..o ..o ..o      | * 4 | 0 0  0  4 2 |  0  0 2 4 4  4 1 | 0 0 0 2 4  4  8 | 0 1 4 4
---------------------+-----+-------------+------------------+-----------------+--------
x.. ... ... ...    & | 2 0 | 4 *  *  * * |  4  0 2 0 0  0 0 | 2 2 0 1 0  4  0 | 1 2 2 0
... ... x.. ...    & | 2 0 | * 4  *  * * |  0  4 0 2 0  0 0 | 0 2 2 0 1  0  4 | 1 0 2 2
oo. oo. oo. oo.&#x   | 2 0 | * * 16  * * |  2  2 0 0 0  1 0 | 1 2 1 0 0  2  2 | 1 1 2 1
o.o o.o o.o o.o&#x & | 1 1 | * *  * 16 * |  0  0 1 1 1  2 0 | 0 0 0 1 1  3  4 | 0 1 3 2
... ... ..x ...      | 0 2 | * *  *  * 4 |  0  0 0 2 2  0 1 | 0 0 0 1 4  0  4 | 0 0 2 4
---------------------+-----+-------------+------------------+-----------------+--------
xo. ... ... ...&#x & | 3 0 | 1 0  2  0 0 | 16  * * * *  * * | 1 1 0 0 0  1  0 | 1 1 1 0
... ... xo. ...&#x & | 3 0 | 0 1  2  0 0 |  * 16 * * *  * * | 0 1 1 0 0  0  1 | 1 0 1 1
x.o ... ... ...&#x & | 2 1 | 1 0  0  2 0 |  *  * 8 * *  * * | 0 0 0 1 0  2  0 | 0 1 2 0
... ... x.x ...&#x & | 2 2 | 0 1  0  2 1 |  *  * * 8 *  * * | 0 0 0 0 1  0  2 | 0 0 1 2
... ... ... o.x&#x & | 1 2 | 0 0  0  2 1 |  *  * * * 8  * * | 0 0 0 1 1  0  2 | 0 0 2 2
ooo ooo ooo ooo&#x   | 2 1 | 0 0  1  2 0 |  *  * * * * 16 * | 0 0 0 0 0  2  2 | 0 1 2 1
... ... ..x ..x      | 0 4 | 0 0  0  0 4 |  *  * * * *  * 1 | 0 0 0 0 4  0  0 | 0 0 0 4
---------------------+-----+-------------+------------------+-----------------+--------
xo. ox. ... ...&#x   ♦ 4 0 | 2 0  4  0 0 |  4  0 0 0 0  0 0 | 4 * * * *  *  * | 1 1 0 0
xo. ... ... ox.&#x & ♦ 4 0 | 1 1  4  0 0 |  2  2 0 0 0  0 0 | * 8 * * *  *  * | 1 0 1 0
... ... xo. ox.&#x   ♦ 4 0 | 0 2  4  0 0 |  0  4 0 0 0  0 0 | * * 4 * *  *  * | 1 0 0 1
x.o ... ... o.x&#x & ♦ 2 2 | 1 0  0  4 1 |  0  0 2 0 2  0 0 | * * * 4 *  *  * | 0 0 2 0
... ... x.x o.x&#x & ♦ 2 4 | 0 1  0  4 4 |  0  0 0 2 2  0 1 | * * * * 4  *  * | 0 0 0 2
xoo ... ... ...&#x & ♦ 3 1 | 1 0  2  3 0 |  1  0 1 0 0  2 0 | * * * * * 16  * | 0 1 1 0
... ... xox ...&#x & ♦ 3 2 | 0 1  2  4 1 |  0  1 0 1 1  2 0 | * * * * *  * 16 | 0 0 1 1
---------------------+-----+-------------+------------------+-----------------+--------
xo. ox. xo. ox.&#zx  ♦ 8 0 | 4 4 16  0 0 | 16 16 0 0 0  0 0 | 4 8 4 0 0  0  0 | 1 * * *
xoo oxo ... ...&#x & ♦ 4 1 | 2 0  4  4 0 |  4  0 2 0 0  4 0 | 1 0 0 0 0  4  0 | * 4 * *
xoo ... ... oxx&#x & ♦ 4 2 | 1 1  4  6 1 |  2  2 2 1 2  4 0 | 0 1 0 1 0  2  2 | * * 8 *
... ... xox oxx&#x   ♦ 4 4 | 0 2  4  8 4 |  0  4 0 4 4  4 1 | 0 0 1 0 2  0  4 | * * * 4
```

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