Acronym rapt
Name rectified-pentachoric (line-)tegum,
rectified-pentachoric dipyramid
Circumradius ...
Lace city
in approx. ASCII-art 
  O   o       o = o3o3o
              O = o3x3o
o   T         T = x3o3o
Dihedral angles
(at margins)
  • at oct between octpy and octpy:   arccos(-3/5) = 126.869898°
  • at tet between octpy and pen:   arccos[-1/sqrt(5)] = 116.565051°
  • at tet between pen and pen:   arccos(-7/25) = 106.260205°
  • at tet between octpy and octpy:   90°
Face vector 12, 50, 90, 70, 20
Confer
mono-pyramid:
rappy  

Incidence matrix according to Dynkin symbol

ooo3oxo3ooo3ooo&#xt   → both heights = sqrt(2/5) = 0.632456
(pt || pseudo rap || pt)

o..3o..3o..3o..     & | 2  * ♦ 10  0 | 30  0  0 | 10 20 0 0 |  5  5
.o.3.o.3.o.3.o.       | * 10 ♦  2  6 | 12  3  6 |  6 12 3 2 |  6  4
----------------------+------+-------+----------+-----------+------
oo.3oo.3oo.3oo.&#x  & | 1  1 | 20  * ♦  6  0  0 |  3  6 0 0 |  3  2
... .x. ... ...       | 0  2 |  * 30 |  2  1  2 |  2  4 2 1 |  4  2
----------------------+------+-------+----------+-----------+------
... ox. ... ...&#x  & | 1  2 |  2  1 | 60  *  * |  1  2 0 0 |  2  1
.o.3.x. ... ...       | 0  3 |  0  3 |  * 10  * |  2  0 2 0 |  4  0
... .x.3.o. ...       | 0  3 |  0  3 |  *  * 20 |  0  2 1 1 |  2  2
----------------------+------+-------+----------+-----------+------
oo.3ox. ... ...&#x  & ♦ 1  3 |  3  3 |  3  1  0 | 20  * * * |  2  0
... ox.3oo. ...&#x  & ♦ 1  3 |  3  3 |  3  0  1 |  * 40 * * |  1  1
.o.3.x.3.o. ...       ♦ 0  6 |  0 12 |  0  4  4 |  *  * 5 * |  2  0
... .x.3.o.3.o.       ♦ 0  4 |  0  6 |  0  0  4 |  *  * * 5 |  0  2
----------------------+------+-------+----------+-----------+------
oo.3ox.3oo. ...&#x  & ♦ 1  6 |  6 12 | 12  4  4 |  4  4 1 0 | 10  *
... ox.3oo.3oo.&#x  & ♦ 1  4 |  4  6 |  6  0  4 |  0  4 0 1 |  * 10

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