Acronym state
Name stellar tettene,
pentagrammic tettene,
pentagram-pyramidal pyramid pyramid,
triangle atop fully orthogonal pentagram
Circumradius sqrt[(1+sqrt(5))/8] = 0.636010
Dual (topologically selfdual, in different orientation)
Confer
related segmentotera:
{5/2} || perp {5/2} (stadow)   {4} || perp {5/2} (sistadow)  
general polytopal classes:
segmentotera   tettene  

Incidence matrix according to Dynkin symbol

ooox5/2oooo&#x   → height(1,2) = height(1,3) = height(2,3) = 1
                   height(1,4) = height(2,4) = height(3,4) = sqrt((5+sqrt(5))/10) = 0.850651
(pyramid product of {3} with {5/2})

o...5/2o...    | 1 * * *  1 1 5 0 0 0 0 | 1 5 5 5 0 0 0 0 | 5 5 5 1 0 0 0 | 5 1 1 0
.o..5/2.o..    | * 1 * *  1 0 0 1 5 0 0 | 1 5 0 0 5 5 0 0 | 5 5 0 0 5 1 0 | 5 1 0 1
..o.5/2..o.    | * * 1 *  0 1 0 1 0 5 0 | 1 0 5 0 5 0 5 0 | 5 0 5 0 5 0 1 | 5 0 1 1
...o5/2...o    | * * * 5 | 0 0 1 0 1 1 2 | 0 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1
---------------+---------+---------------+-----------------+---------------+--------
oo..5/2oo..&#x | 1 1 0 0 | 1 * * * * * *  1 5 0 0 0 0 0 0 | 5 5 0 0 0 0 0 | 5 1 0 0
o.o.5/2o.o.&#x | 1 0 1 0 | * 1 * * * * *  1 0 5 0 0 0 0 0 | 5 0 5 0 0 0 0 | 5 0 1 0
o..o5/2o..o&#x | 1 0 0 1 | * * 5 * * * * | 0 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
.oo.5/2.oo.&#x | 0 1 1 0 | * * * 1 * * *  1 0 0 0 5 0 0 0 | 5 0 0 0 5 0 0 | 5 0 0 1
.o.o5/2.o.o&#x | 0 1 0 1 | * * * * 5 * * | 0 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1
..oo5/2..oo&#x | 0 0 1 1 | * * * * * 5 * | 0 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1
...x   ....    | 0 0 0 2 | * * * * * * 5 | 0 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
---------------+---------+---------------+-----------------+---------------+--------
ooo.5/2ooo.&#x | 1 1 1 0 | 1 1 0 1 0 0 0 | 1 * * * * * * * | 5 0 0 0 0 0 0 | 5 0 0 0
oo.o5/2oo.o&#x | 1 1 0 1 | 1 0 1 0 1 0 0 | * 5 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
o.oo5/2o.oo&#x | 1 0 1 1 | 0 1 1 0 0 1 0 | * * 5 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0
o..x   ....&#x | 1 0 0 2 | 0 0 2 0 0 0 1 | * * * 5 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.ooo5/2.ooo&#x | 0 1 1 1 | 0 0 0 1 1 1 0 | * * * * 5 * * * | 1 0 0 0 2 0 0 | 2 0 0 1
.o.x   ....&#x | 0 1 0 2 | 0 0 0 0 2 0 1 | * * * * * 5 * * | 0 1 0 0 1 1 0 | 1 1 0 1
..ox   ....&#x | 0 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * 5 * | 0 0 1 0 1 0 1 | 1 0 1 1
...x5/2...o    | 0 0 0 5 | 0 0 0 0 0 0 5 | * * * * * * * 1 | 0 0 0 1 0 1 1 | 0 1 1 1  {5/2}
---------------+---------+---------------+-----------------+---------------+--------
oooo5/2oooo&#x  1 1 1 1 | 1 1 1 1 1 1 0 | 1 1 1 0 1 0 0 0 | 5 * * * * * * | 2 0 0 0
oo.x   ....&#x  1 1 0 2 | 1 0 2 0 2 0 1 | 0 2 0 1 0 1 0 0 | * 5 * * * * * | 1 1 0 0
o.ox   ....&#x  1 0 1 2 | 0 1 2 0 0 2 1 | 0 0 2 1 0 0 1 0 | * * 5 * * * * | 1 0 1 0
o..x5/2o..o&#x  1 0 0 5 | 0 0 5 0 0 0 5 | 0 0 0 5 0 0 0 1 | * * * 1 * * * | 0 1 1 0
.oox   ....&#x  0 1 1 2 | 0 0 0 1 2 2 1 | 0 0 0 0 2 1 1 0 | * * * * 5 * * | 1 0 0 1
.o.x5/2.o.o&#x  0 1 0 5 | 0 0 0 0 5 0 5 | 0 0 0 0 0 5 0 1 | * * * * * 1 * | 0 1 0 1
..ox5/2..oo&#x  0 0 1 5 | 0 0 0 0 0 5 5 | 0 0 0 0 0 0 5 1 | * * * * * * 1 | 0 0 1 1
---------------+---------+---------------+-----------------+---------------+--------
ooox   ....&#x  1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 0 | 2 1 1 0 1 0 0 | 5 * * *
oo.x5/2oo.o&#x  1 1 0 5 | 1 0 5 0 5 0 5 | 0 5 0 5 0 5 0 1 | 0 5 0 1 0 1 0 | * 1 * *
o.ox5/2o.oo&#x  1 0 1 5 | 0 1 5 0 0 5 5 | 0 0 5 5 0 0 5 1 | 0 0 5 1 0 0 1 | * * 1 *
.oox5/2.ooo&#x  0 1 1 5 | 0 0 0 1 5 5 5 | 0 0 0 0 5 5 5 1 | 0 0 0 0 5 1 1 | * * * 1
or
o...5/2o...    & | 3 *  2  5 0 | 1 10  5 0 | 5 10 1 | 5 2
...o5/2...o      | * 5 | 0  3 2 | 0  3  6 1 | 1  6 3 | 2 3
-----------------+-----+--------+-----------+--------+----
oo..5/2oo..&#x & | 2 0 | 3  * *  1  5  0 0 | 5  5 0 | 5 1
o..o5/2o..o&#x & | 1 1 | * 15 * | 0  2  2 0 | 1  4 1 | 2 2
...x   ....      | 0 2 | *  * 5 | 0  0  3 1 | 0  3 3 | 1 3
-----------------+-----+--------+-----------+--------+----
ooo.5/2ooo.&#x   | 3 0 | 3  0 0 | 1  *  * * | 5  0 0 | 3 0
oo.o5/2oo.o&#x & | 2 1 | 1  2 0 | * 15  * * | 1  2 0 | 2 1
o..x   ....&#x & | 1 2 | 0  2 1 | *  * 15 * | 0  2 1 | 1 2
...x5/2...o      | 0 5 | 0  0 5 | *  *  * 1 | 0  0 3 | 0 3  {5/2}
-----------------+-----+--------+-----------+--------+----
oooo5/2oooo&#x    3 1 | 3  3 0 | 1  3  0 0 | 5  * * | 2 0
oo.x   ....&#x &  2 2 | 1  4 1 | 0  2  2 0 | * 15 * | 1 1
o..x5/2o..o&#x &  1 5 | 0  5 5 | 0  0  5 1 | *  * 3 | 0 2
-----------------+-----+--------+-----------+--------+----
ooox   ....&#x    3 2 | 3  6 1 | 1  6  3 0 | 2  3 0 | 5 *
oo.x5/2oo.o&#x &  2 5 | 1 10 5 | 0  5 10 1 | 0  5 2 | * 3

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