(old: great double antiprism – but not: great antiprism)
© net of gudap (overlapping in space)
©
©
- more general:
- sns2sms
- uniform relatives:
- sishi distadedip
- compounds:
- ditsop
links
| Acronym | gudap (old: gedap) |
| Name |
great duoantiprism, (old: great double antiprism – but not: great antiprism) |
| |
| Cross sections |
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| Circumradius | 1 |
| Vertex figure |
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| Face vector | 50, 200, 220, 70 |
| Confer |
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External links |
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As abstract polytope gudap is automorph, thereby interchanging the roles of pentagons and pentagrams, resp. those of pap and starp. – None the less there is an (only isogonal) isomorph too, pedap, then replacing pentagrams by pentagons, resp. replacing starp by a variant of pap as well (and accordingly the tet becomes a subsymmetric disphenoid only as well).
Besides of s2s2s2s (hex, the alternated vertex faceting of tes) this is the only other possible alternated vertex faceting of an (omnitruncated) duoprism, which can be made uniform.
Alternatively it can be obtained as a subsymmetrical faceting of sishi. Note that its edge skeleton supports not only sissid or gike cells, but also gad or ike cells. Therefore choose from sishi any single ring of 10 sissids. That then well could be replaced by a ring of starps. The then open faces could be closed by a complemental ring of 10 paps – up to some "glue" of 50 tets.
Incidence matrix according to Dynkin symbol
s5s2s5/3s
demi( . . . . ) | 50 | 1 1 1 1 2 2 | 1 1 3 3 3 3 | 1 1 1 1 4
------------------+----+-------------------+-------------------+-----------
s 2 s . | 2 | 25 * * * * * | 0 0 2 0 2 0 | 1 0 1 0 2
s . 2 s | 2 | * 25 * * * * | 0 0 0 2 2 0 | 0 1 1 0 2
. s2s . | 2 | * * 25 * * * | 0 0 2 0 0 2 | 1 0 0 1 2
. s 2 s | 2 | * * * 25 * * | 0 0 0 2 0 2 | 0 1 0 1 2
sefa( s5s . . ) | 2 | * * * * 50 * | 1 0 1 1 0 0 | 1 1 0 0 1
sefa( . . s5/3s ) | 2 | * * * * * 50 | 0 1 0 0 1 1 | 0 0 1 1 1
------------------+----+-------------------+-------------------+-----------
s5s . . | 5 | 0 0 0 0 5 0 | 10 * * * * * | 1 1 0 0 0
. . s5/3s | 5 | 0 0 0 0 0 5 | * 10 * * * * | 0 0 1 1 0
sefa( s5s2s . ) | 3 | 1 0 1 0 1 0 | * * 50 * * * | 1 0 0 0 1
sefa( s5s 2 s ) | 3 | 0 1 0 1 1 0 | * * * 50 * * | 0 1 0 0 1
sefa( s 2 s5/3s ) | 3 | 1 1 0 0 0 1 | * * * * 50 * | 0 0 1 0 1
sefa( . s2s5/3s ) | 3 | 0 0 1 1 0 1 | * * * * * 50 | 0 0 0 1 1
------------------+----+-------------------+-------------------+-----------
s5s2s . ♦ 10 | 5 0 5 0 10 0 | 2 0 10 0 0 0 | 5 * * * *
s5s 2 s ♦ 10 | 0 5 0 5 10 0 | 2 0 0 10 0 0 | * 5 * * *
s 2 s5/3s ♦ 10 | 5 5 0 0 0 10 | 0 2 0 0 10 0 | * * 5 * *
. s2s5/3s ♦ 10 | 0 0 5 5 0 10 | 0 2 0 0 0 10 | * * * 5 *
sefa( s5s2s5/3s ) ♦ 4 | 1 1 1 1 1 1 | 0 0 1 1 1 1 | * * * * 50
or
demi( . . . . ) | 50 | 4 2 2 | 1 1 6 6 | 2 2 4
--------------------+----+-----------+---------------+---------
s 2 s . & | 2 | 100 * * | 0 0 2 2 | 1 1 2
sefa( s5s . . ) | 2 | * 50 * | 1 0 2 0 | 2 0 1
sefa( . . s5/3s ) | 2 | * * 50 | 0 1 0 2 | 0 2 1
--------------------+----+-----------+---------------+---------
s5s . . | 5 | 0 5 0 | 10 * * * | 2 0 0
. . s5/3s | 5 | 0 0 5 | * 10 * * | 0 2 0
sefa( s5s2s . ) & | 3 | 2 1 0 | * * 100 * | 1 0 1
sefa( s 2 s5/3s ) & | 3 | 2 0 1 | * * * 100 | 0 1 1
--------------------+----+-----------+---------------+---------
s5s2s . & ♦ 10 | 10 10 0 | 2 0 10 0 | 10 * *
s 2 s5/3s & ♦ 10 | 10 0 10 | 0 2 0 10 | * 10 *
sefa( s5s2s5/3s ) ♦ 4 | 4 1 1 | 0 0 2 2 | * * 50
starting figure: x5x x5/3x
xo5ox xo5/3ox&#zx → height = 0 (tegum sum of 2 bidual starpedips) o.5o. o.5/3o. | 25 * | 2 2 4 0 0 | 1 1 4 2 4 2 0 0 | 2 2 2 2 .o5.o .o5/3.o | * 25 | 0 0 4 2 2 | 0 0 2 4 2 4 1 1 | 2 2 2 2 ------------------+-------+-----------------+---------------------+------------ x. .. .. .. | 2 0 | 25 * * * * | 1 0 2 0 0 0 0 0 | 2 1 0 0 .. .. x. .. | 2 0 | * 25 * * * | 0 1 0 0 2 0 0 0 | 0 0 1 2 oo5oo oo5/3oo&#x | 1 1 | * * 100 * * | 0 0 1 1 1 1 0 0 | 1 1 1 1 .. .x .. .. | 0 2 | * * * 25 * | 0 0 0 2 0 0 1 0 | 2 0 1 0 .. .. .. .x | 0 2 | * * * * 25 | 0 0 0 0 0 2 0 1 | 0 1 0 2 ------------------+-------+-----------------+---------------------+------------ x.5o. .. .. | 5 0 | 5 0 0 0 0 | 5 * * * * * * * | 2 0 0 0 .. .. x.5/3o. | 5 0 | 0 5 0 0 0 | * 5 * * * * * * | 0 0 0 2 xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * 50 * * * * * | 1 1 0 0 .. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * 50 * * * * | 1 0 1 0 .. .. xo. ..&#x | 2 1 | 0 1 2 0 0 | * * * * 50 * * * | 0 0 1 1 .. .. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * * 50 * * | 0 1 0 1 .o5.x .. .. | 0 5 | 0 0 0 5 0 | * * * * * * 5 * | 2 0 0 0 .. .. .o5/3.x | 0 5 | 0 0 0 0 5 | * * * * * * * 5 | 0 0 0 2 ------------------+-------+-----------------+---------------------+------------ xo5ox .. ..&#x ♦ 5 5 | 5 0 10 5 0 | 1 0 5 5 0 0 1 0 | 10 * * * xo .. .. ox&#x ♦ 2 2 | 1 0 4 0 1 | 0 0 2 0 0 2 0 0 | * 25 * * .. ox xo ..&#x ♦ 2 2 | 0 1 4 1 0 | 0 0 0 2 2 0 0 0 | * * 25 * .. .. xo5/3ox&#x ♦ 5 5 | 0 5 10 0 5 | 0 1 0 0 5 5 0 1 | * * * 10
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