Acronym	tip (alt: tettum)
Name	truncated pentachoron, tet-based tutsatope, tet-based tutism
	©
Cross sections	©
Circumradius	sqrt(8/5) = 1.264911
Inradius wrt. tet	7/sqrt(40) = 1.106797
Inradius wrt. tut	3/sqrt(40) = 0.474342
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o o3o3o . o3o . o o . o3o . o3o3o 1 x3x3o3o x3x3o . tut first x3x . o {6} first x . o3o edge first . x3o3o tet first 2 u3o3o . u3o . x u . x3o . u3o3o 3 x3o3o . opposite tet x3o . u x . u3o . x3x3o opposite tut 4   o3o . x opposite edge o . x3x opposite {6}
Lace city in approx. ASCII-art	o3o x3o -- x3o3o (tet) o3o u3o -- u3o3o (u-tet) x3o u3o x3x -- x3x3o (tut)
	x o o x -- x3o3o (tet) u o o u -- u3o3o (u-tet) x o u x x u o x -- x3x3o (tut)
Volume	19 sqrt(5)/24 = 1.770220
Surface	10 sqrt(2) = 14.142136
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: tet tut tip 5 5 )
Dihedral angles	at {3} between tet and tut:   arccos(-1/4) = 104.477512° at {6} between tut and tut:   arccos(1/4) = 75.522488°
Dual	m3m3o3o
Face vector	20, 40, 30, 10
Confer	related CRFs: co || (u,x)-co || toe   compounds: tisted   general polytopal classes: Wythoffian polychora   tutsatopes   bistratic lace towers   lace simplices   analogs: truncated simplex tSn   truncated Gossetic t(2n,1)   truncated Gossetic t(1n,2)
External links

Note that tip can be thought of as the external blend of 1 rap + 5 tet || inv tut + 10 pens + 5 raps. This decomposition is described as the (also subdimensioanlly) degenerate segmentoteron ox3ox3xo3oo&#x.

Incidence matrix according to Dynkin symbol

x3x3o3o

. . . . | 20 |  1  3 |  3  3 | 3 1
--------+----+-------+-------+----
x . . . |  2 | 10  * |  3  0 | 3 0
. x . . |  2 |  * 30 |  1  2 | 2 1
--------+----+-------+-------+----
x3x . . |  6 |  3  3 | 10  * | 2 0
. x3o . |  3 |  0  3 |  * 20 | 1 1
--------+----+-------+-------+----
x3x3o . ♦ 12 |  6 12 |  4  4 | 5 *
. x3o3o ♦  4 |  0  6 |  0  4 | * 5

snubbed forms: β3x3o3o, x3β3o3o, β3β3o3o

x3x3o3/2o

. . .   . | 20 |  1  3 |  3  3 | 3 1
----------+----+-------+-------+----
x . .   . |  2 | 10  * |  3  0 | 3 0
. x .   . |  2 |  * 30 |  1  2 | 2 1
----------+----+-------+-------+----
x3x .   . |  6 |  3  3 | 10  * | 2 0
. x3o   . |  3 |  0  3 |  * 20 | 1 1
----------+----+-------+-------+----
x3x3o   . ♦ 12 |  6 12 |  4  4 | 5 *
. x3o3/2o ♦  4 |  0  6 |  0  4 | * 5

x3x3/2o3o

. .   . . | 20 |  1  3 |  3  3 | 3 1
----------+----+-------+-------+----
x .   . . |  2 | 10  * |  3  0 | 3 0
. x   . . |  2 |  * 30 |  1  2 | 2 1
----------+----+-------+-------+----
x3x   . . |  6 |  3  3 | 10  * | 2 0
. x3/2o . |  3 |  0  3 |  * 20 | 1 1
----------+----+-------+-------+----
x3x3/2o . ♦ 12 |  6 12 |  4  4 | 5 *
. x3/2o3o ♦  4 |  0  6 |  0  4 | * 5

x3x3/2o3/2o

. .   .   . | 20 |  1  3 |  3  3 | 3 1
------------+----+-------+-------+----
x .   .   . |  2 | 10  * |  3  0 | 3 0
. x   .   . |  2 |  * 30 |  1  2 | 2 1
------------+----+-------+-------+----
x3x   .   . |  6 |  3  3 | 10  * | 2 0
. x3/2o   . |  3 |  0  3 |  * 20 | 1 1
------------+----+-------+-------+----
x3x3/2o   . ♦ 12 |  6 12 |  4  4 | 5 *
. x3/2o3/2o ♦  4 |  0  6 |  0  4 | * 5

xux3oox3ooo&#xt   → both heights = sqrt(5/8) = 0.790569
(tet || pseudo u-tet || tut)

o..3o..3o..     | 4 *  * | 3 1  0 0  0 | 3 3  0 0 0 | 1 3 0 0
.o.3.o.3.o.     | * 4  * | 0 1  3 0  0 | 0 3  3 0 0 | 0 3 1 0
..o3..o3..o     | * * 12 | 0 0  1 1  2 | 0 1  2 2 1 | 0 2 1 1
----------------+--------+-------------+------------+--------
x.. ... ...     | 2 0  0 | 6 *  * *  * | 2 1  0 0 0 | 1 2 0 0
oo.3oo.3oo.&#x  | 1 1  0 | * 4  * *  * | 0 3  0 0 0 | 0 3 0 0
.oo3.oo3.oo&#x  | 0 1  1 | * * 12 *  * | 0 1  2 0 0 | 0 2 1 0
..x ... ...     | 0 0  2 | * *  * 6  * | 0 1  0 2 0 | 0 2 0 1
... ..x ...     | 0 0  2 | * *  * * 12 | 0 0  1 1 1 | 0 1 1 1
----------------+--------+-------------+------------+--------
x..3o.. ...     | 3 0  0 | 3 0  0 0  0 | 4 *  * * * | 1 1 0 0
xux ... ...&#xt | 2 2  2 | 1 2  2 1  0 | * 6  * * * | 0 2 0 0
... .ox ...&#x  | 0 1  2 | 0 0  2 0  1 | * * 12 * * | 0 1 1 0
..x3..x ...     | 0 0  6 | 0 0  0 3  3 | * *  * 4 * | 0 1 0 1
... ..x3..o     | 0 0  3 | 0 0  0 0  3 | * *  * * 4 | 0 0 1 1
----------------+--------+-------------+------------+--------
x..3o..3o..     ♦ 4 0  0 | 6 0  0 0  0 | 4 0  0 0 0 | 1 * * *
xux3oox ...&#xt ♦ 3 3  6 | 3 3  6 3  3 | 1 3  3 1 0 | * 4 * *
... .ox3.oo&#x  ♦ 0 1  3 | 0 0  3 0  3 | 0 0  3 0 1 | * * 4 *
..x3..x3..o     ♦ 0 0 12 | 0 0  0 6 12 | 0 0  0 4 4 | * * * 1

xuxo oxux3ooox&#xt   → all heights = sqrt(5/12) = 0.645497
(line || pseudo u-laced trip || pseudo u-based trip || (ortho) {6})

o... o...3o...     | 2 * * * | 1 3 0 0 0  0 0 0 | 3 3 0 0 0 0 0 | 1 3 0 0
.o.. .o..3.o..     | * 6 * * | 0 1 2 1 0  0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0
..o. ..o.3..o.     | * * 6 * | 0 0 0 1 1  2 0 0 | 0 1 0 2 2 1 0 | 0 2 1 1
...o ...o3...o     | * * * 6 | 0 0 0 0 0  2 1 1 | 0 0 0 2 1 2 1 | 0 1 2 1
-------------------+---------+------------------+---------------+--------
x... .... ....     | 2 0 0 0 | 1 * * * *  * * * | 0 3 0 0 0 0 0 | 0 3 0 0
oo.. oo..3oo..&#x  | 1 1 0 0 | * 6 * * *  * * * | 2 1 0 0 0 0 0 | 1 2 0 0
.... .x.. ....     | 0 2 0 0 | * * 6 * *  * * * | 1 0 1 1 0 0 0 | 1 1 1 0
.oo. .oo.3.oo.&#x  | 0 1 1 0 | * * * 6 *  * * * | 0 1 0 2 0 0 0 | 0 2 1 0
..x. .... ....     | 0 0 2 0 | * * * * 3  * * * | 0 1 0 0 2 0 0 | 0 2 0 1
..oo ..oo3..oo&#x  | 0 0 1 1 | * * * * * 12 * * | 0 0 0 1 1 1 0 | 0 1 1 1
.... ...x ....     | 0 0 0 2 | * * * * *  * 3 * | 0 0 0 2 0 0 1 | 0 1 2 0
.... .... ...x     | 0 0 0 2 | * * * * *  * * 3 | 0 0 0 0 0 2 1 | 0 0 2 1
-------------------+---------+------------------+---------------+--------
.... ox.. ....&#x  | 1 2 0 0 | 0 2 1 0 0  0 0 0 | 6 * * * * * * | 1 1 0 0
xux. .... ....&#xt | 2 2 2 0 | 1 2 0 2 1  0 0 0 | * 3 * * * * * | 0 2 0 0
.... .x..3.o..     | 0 3 0 0 | 0 0 3 0 0  0 0 0 | * * 2 * * * * | 1 0 1 0
.... .xux ....&#xt | 0 2 2 2 | 0 0 1 2 0  2 1 0 | * * * 6 * * * | 0 1 1 0
..xo .... ....&#x  | 0 0 2 1 | 0 0 0 0 1  2 0 0 | * * * * 6 * * | 0 1 0 1
.... .... ..ox&#x  | 0 0 1 2 | 0 0 0 0 0  2 0 1 | * * * * * 6 * | 0 0 1 1
.... ...x3...x     | 0 0 0 6 | 0 0 0 0 0  0 3 3 | * * * * * * 1 | 0 0 2 0
-------------------+---------+------------------+---------------+--------
.... ox..3oo..&#x  ♦ 1 3 0 0 | 0 3 3 0 0  0 0 0 | 3 0 1 0 0 0 0 | 2 * * *
xuxo oxux ....&#xt ♦ 2 4 4 2 | 1 4 2 4 2  4 1 0 | 2 2 0 2 2 0 0 | * 3 * *
.... .xux3.oox&#xt ♦ 0 3 3 6 | 0 0 3 3 0  6 3 3 | 0 0 1 3 0 3 1 | * * 2 *
..xo .... ..ox&#x  ♦ 0 0 2 2 | 0 0 0 0 1  4 0 1 | 0 0 0 0 2 2 0 | * * * 3