Acronym sidtidap
Name small-ditrigonal-icosidodecahedron antiprism
Cross sections
 ©
Circumradius sqrt[(27+sqrt(5))/32] = 0.955838
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: ditdid gidtid pap sidtid stap tet
ditdidap 20120120
gidtidap 02120040
sidtidap 00021240
all 3 members of this regiment where first described by N. Johnson and accordingly are known also as Johnson antiprisms.)
External
links
hedrondude   WikiChoron  

As abstract polytope sidtidap is isomorphic to gidtidap, thereby replacing pentagrams by pentagons, resp. stap by pap and sidtid by gidtid.

In fact, this polychoron generalizes the idea of a 3D antiprism by way of being a snub (here: holosnub). But this figure is not what now became the accepted sense of a 4D antiprism, where its bases have to be duals of each other. It rather looks more like what was coined as cupola (in its narrower sense), i.e. the xoPoxQoo&#x segmentochora, as it uses pyramids and antiprisms for lacing facets only. (But pyramids do point here in both directions, so.)


Incidence matrix according to Dynkin symbol

β2β5o3o

both( . . . . ) | 40 |  3   6 |  3   9  3 |  3 1  4
----------------+----+--------+-----------+--------
both( s2s . . ) |  2 | 60   * |  0   4  0 |  2 0  2
sefa( . β5o . ) |  2 |  * 120 |  1   1  1 |  1 1  1
----------------+----+--------+-----------+--------
      . β5o .     5 |  0   5 | 24   *  * |  1 1  0
sefa( β2β5o . ) |  3 |  2   1 |  * 120  * |  1 0  1
sefa( . β5o3o ) |  3 |  0   3 |  *   * 40 |  0 1  1
----------------+----+--------+-----------+--------
      β2β5o .    10 | 10  10 |  2  10  0 | 12 *  *
      . β5o3o    20 |  0  60 | 12   0 20 |  * 2  *
sefa( β2β5o3o )   4 |  3   3 |  0   3  1 |  * * 40

starting figure: x x5o3o

xo5/2ox3oo3*a&#x   → height = (1+sqrt(5))/4 = 0.809017

o.   o. o.       | 20  * |  6  3  0 |  3  3  6  3  0  0 | 1  3  3  1 0
.o   .o .o       |  * 20 |  0  3  6 |  0  0  3  6  3  3 | 0  3  1  3 1
-----------------+-------+----------+-------------------+-------------
x.   .. ..       |  2  0 | 60  *  * |  1  1  1  0  0  0 | 1  1  1  0 0
oo5/2oo3oo3*a&#x |  1  1 |  * 60  * |  0  0  2  2  0  0 | 0  2  1  1 0
..   .x ..       |  0  2 |  *  * 60 |  0  0  0  1  1  1 | 0  1  0  1 1
-----------------+-------+----------+-------------------+-------------
x.5/2o. ..       |  5  0 |  5  0  0 | 12  *  *  *  *  * | 1  1  0  0 0
x.   .. o.3*a    |  3  0 |  3  0  0 |  * 20  *  *  *  * | 1  0  1  0 0
xo   .. ..   &#x |  2  1 |  1  2  0 |  *  * 60  *  *  * | 0  1  1  0 0
..   ox ..   &#x |  1  2 |  0  2  1 |  *  *  * 60  *  * | 0  1  0  1 0
.o5/2.x ..       |  0  5 |  0  0  5 |  *  *  *  * 12  * | 0  1  0  0 1
..   .x3.o       |  0  3 |  0  0  3 |  *  *  *  *  * 20 | 0  0  0  1 1
-----------------+-------+----------+-------------------+-------------
x.5/2o.3o.3*a     20  0 | 60  0  0 | 12 20  0  0  0  0 | 1  *  *  * *
xo5/2ox ..   &#x   5  5 |  5 10  5 |  1  0  5  5  1  0 | * 12  *  * *
xo   .. oo3*a&#x   3  1 |  3  3  0 |  0  1  3  0  0  0 | *  * 20  * *
..   ox3oo   &#x   1  3 |  0  3  3 |  0  0  0  3  0  1 | *  *  * 20 *
.o5/2.x3.o3*a      0 20 |  0  0 60 |  0  0  0  0 12 20 | *  *  *  * 1

© 2004-2014
top of page