Discord Discovery Wave

Sad Taspodady VerfTocap VerfGidpaxhi Prarsi Blend VerfPecuexdap VerfSiggisdah VerfHorrible Pseudo Uniform Verf

Above are the verfs of sad taspodady (a sidtaxhi scaliform), tocap (a gudap regiment scaliform), a gidipthi scaliform verf, pecuexdap verf (one of the new uniform polychora), siggisdah verf (one of the idtessids), and the verf of 'Oh HELL Gnaw' - a pseudo-uniform formed by blending several rissid swirlprisms. Below are slice animations of sad taspodady, the fever dream (an ixoic isogonal), the 27/10 Hemiantiprism from infinite scaliform category SA, pecuexdap, siggissido (one of the core idtessids), tocap, a pseudo-uniform rissid swirlprism, sispaxthiccudy - a padohi diminishing which is scaliform, and a grid swirler isogonal with 23-swirldoic symmetry. These animations were made with Stella4D.

Slices of Sad TaspodadyFever Dream27/10 HAPPequexdapSiggissidoTocapRissid SwirlprismSispaxthiccudyGrid Swirler 23


What started as a place for polytope enthusiast to talk about polytopes - Polytope Discord - lead to an accellerating rush of new discoveries which dwarfed the Pedisna Discovery Wave, this was the biggest rush of discoveries since my own in the 90's which would double the scaliform categories, and even add the elusive 'Category 30' to the uniform polychora. Other finds include isogonal polytopes, the Eldritch Horror Snubs in dimensions 7 and 8, subsymmetric facetings of naq, and many others. This wave of discoveries was moving so fast, that I had trouble keeping up! I will describe this incredible wave of discovery in the order that it happened.

The Quiet Before The Storm

February 12, 2020 - Spirit Backup started the Polytope Discord, he quickly invited Richard Klitzing, Wendy Krieger, and myself to join. Many others such as Username 5243, Mecejide, Grand Antiprism, and URL will join afterwards. This was before my last website update on Feb. 29 and well before the discovery wave.

March 13-21, 2020 - After finding some subsymmetric compounds in the naq regiment, including one later called 'rush', Mecejide found that they can blend with known naq mambers leading to many unknown uniform polyecta in the regiment. Naq is the E7 polytope and these facetings have heic symmetry which is the doubling of the 7-simplex. Over the next few days, I worked on a spreadsheet for the naq regiment and coined many names for the new poytopes, compounds, and fissaries in the regiment. Some of the names for this regiment was quite comical or even tongue in cheek, such as shit, shitter, funpal, slither, flash quiztar, fish sizzler, fart quishez, feqle shizzit, and shizzers. The discord had a blast with these names. I have yet to finish the naq subsymmetrics due to the need to make a complete heic regiment map of naq which I started on the 21st, but didn't complete. On the 19th, I found that some members I had listed were degenerate due to mix-matched rap connections - peaks that had rap split into firp and pinnip.

March 20, 2020 - Username5243 started helping me list out and name uniform polypeta on my spreadsheet.

April 14-18, 2020 - Mecejide announced finding six new uniform polychora and it appeared two actually worked, but they were un-Stellable, I noticed that I had them mentioned amongst the tetrasidpiths in my notes but assumed that they were scaliform. This made the count of uniforms go up to 1851. I also found a compound of rapsady and exes which lead to various uniform compounds containing rapsady. The next day two more uniforms were found by Mecejide bringing count to 1853. On the 18th, I noticed that the four new 'uniforms' may not work after all due to having more vertices than the symmetry would allow, this would also reduce the number of tetrasidpiths. Uniform count stays at 1849.

May 3, 2020 - Discord members started a new polytope Wiki.

May 10, 2020 - URL (also goes by Violet) started rendering starry step prisms. On the 16th, she also started developing Miratope, a polytope rendering software which was used for the starry step prisms.

May 30 - June 11, 2020 - I got the book 'Of Quarternions and Octonions' by John H. Conway and Derek A. Smith which I ordered earlier. I got it primarily to study the 4-D point groups to help me find all of the symmetries in 4 dimensions to eventually write macroes to generate OFF files to generate fair dice and isogonal polychora of any symmetry group. A list of the point groups was mentioned in the book which would help me on that quest. On June 11, I ordered 'Symmetry of Things' which also had the 4-D point groups list and was an easier read.

June 19, 2020 - I made plans to only add several new Making Polychora for my website updates, which I started some new ones - but plans were about to change.


A Storm Slowly Brewing

July 1-21, 2020 - Grand Antiprism (GAP for short) was adding many isogonal polytopes to the new Wiki and was heavily researching them. On the 3rd, I noticed that the IxT and IxO symmetries mentioned in Conway's books had examples that I rendered years ago on Stella, they are the polychora that I called 'the Weird snubs'. On the next day, I coined the names 'ixitic' and 'ixoic' for those two symmetries as well as a few other symmetry short names, like oxitic. I also started teaming up with GAP by loading pics of various isogonals that I had rendered on Stella as he explored various isogonals. On the 13th, I figured that the symmetries of spiddit and sispatit are mentioned in Conway's books as [IxD2n] where n=2 and n=3 respectively. I also rendered cores of these shapes for GAP and later played around with truncating and expanding these cores as well as polychora like afdec to see if they lead to anything interesting. On the 21st, I explored the hulls of subsets of the 10-ex compound under rahi and found all sorts of isogonals and fair dice.

July 25, 2020 - I started to write symmetry macroes to generate OFF files of various isogonal polychora, this would also be very helpful to GAP on his explorations of these. I started with various swirl macroes over the next few days.

August 2, 2020 - The Polytope Discord had a huge influx of newcomers due to a video on YouTube by jan Misali on 48 regular polyhedra. You may recognize the blurred picture of me on his channel :).

August 3-September 2, 2020 - I wrote macros to generate OFF files for ixoic, toxitic, and many other symmetries. I showed many of my renders to GAP on discord. One of the ixoics I called 'the fever dream' and a fair dice that was a horribly distorted cont variant which I nick-named as 'clunker cont'. Over the next two days, I helped GAP investigate various 2-ico isogonals (has the vertices of 2 icoes). I also coded various tessic, pennic, and decaic symmetry macros. On the 7th, GAP and I studied various decaic snubs, I started finding the 'bosids' which have kidecaic symmetry. On the 8th, I drew up the phase map for kidecaic symmetry. On the 9th, I found that there are 45 isogonals in the pennic symmetry family which includes pennic, decaic, kidecaic, kipennic, and iodecaic symmetries. The next day, I worked with contic isogonals and revealed them to GAP who found many of them also. Around this time, Planet N9ne started naming many hyperbolic uniforms and finding various blends. Eric (Polychoron Lover) has also been working on naming Euclideans from an earlier time. On the 11th, I done the toxitic and oxitic symmetry map and found several isogonals in oxitic symmetry which I revealed to GAP the next day. On the 13th, I started the ixitic symmetry map which was one of ten phase maps. I found several wierd looking ixitic isogonals. Over the next several days, I worked with other phase maps of ixitics and shared the results with GAP. On the 24th, I started the ixoic symmetry phase maps. I later found that there were 35 ixoic isogonals in the first phase tet of ixoic symmetry on the 27th. Also studied ixoics with up to 1440 vertices.

September 3, 2020 - Mecejide found the Eldritch Horror Snubs, these are idcossid like blends of various naqic and fyic polytopes in 7 and 8 dimensions. The first one is a blend of 30 naqs in the barz army (hoshostaz) and the second is a 270 fy blend (testy baff) in the bay army. Several others are also suspected.

September 18-23, 2020 - I explored the various swirl symmetry families and the various duoprism symmetries and later coined these names: dippic, kidippic, dukipic, dugypic, dappic, kidappic, dukappic, antidugypic, antikidippic, antiodippic, and gykidippic for them. On the 21st, I coded macroes for various gyrochoron symmetries. On the 23rd, I explored the various extended duoprism symmetries.

September 25, 2020 - Mecejide found that a prissi compound can blend with padohi, leading to scaliform padohis with ixitic symmetry. This adds four new scaliform categories - ixitic padohis, ixitic gidipthis, prissi blended idcossids, and prarsi blended dircospids. These were also found by _Geometer.


A Full Blown Discovery Hurricane

September 30, 2020 - Mecejide investigated the isogonal 20 diminsidhed rat (idrat) and 40 diminished nit (fudnit) which have a gyropentic symmetry. Someone from the hi.gh.er space forum named _Geometer found many new scaliforms including two in the gudap regiment (tocap and gocap). I suggested inviting him to the discord after hearing of a potential uniform polychoron discovery. He soon joined and sent Stella files of the verfs of two brand new uniform polychora - sidditsphit and gidditsphit which are swirlprismattics in the sishi regiment, these are the first new uniform polychora in 14 years. I started blending the verfs of the new uniforms in new ways and found two fissary uniforms and two valid uniforms that forms, leading to the next two uniform polychora - setut and getut which have ixitic symmetry and are also in the sishi regiment. The uniform polychoron count went up to 1853 and these were not false alarms. Geometer had made a PDF listing many scaliforms in the sishi regiment which will be in a new scaliform category - odd celled sishis, he listed more on the next day. He also had found a scaliform in the sidtaxhi regiment along with its conjugate.

October 6-18, 2020 - Following _Geometer's sidtaxhi scaliform, I searched the regiment and found many more sidtaxhi and gadtaxady scaliforms forming two new scaliform categories and potentially a third undiscovered one - dattady scaliforms. On the 8th, I made a regiment map of sidtaxhi under kisispic symmetry and found some kisispic members. On the 10th, I done a thorough search of the sidtaxhis and found 104 figures under the new regiment map including the uniforms (no new ones), compounds, fissaries, and scaliforms. Some of the kisispic scaliforms have sidhids and seihids for cells, the first known to exist other than prisms. These have conjugates in the gadtaxady regiment. On the 13th, I had them listed on my spreadsheet. On the 18th, I started an ixitic padohi regiment map.

October 19-21, 2020 - _Geometer considered blending ico members with sishi. I looked at a blend of an odho verf with sidditsphix on Stella and it worked and was uniform - or so I thought, I later found there were 12 new 'uniform' polychora here by blending in odhos and huhohs in different ways and lead to a polychoron count of 1865 and appeared to create a new category 30 - Gyroic Sishis. Early on the 21st, I found that the 12 new uniforms weren't uniform at all, but were pseudo-uniform similar to the pseudo variant of sirco. Even though their verfs have the same shape, they come in two variants instead of one, so uniform count went back to 1853 and no category 30.

October 23, 2020 - Geometer found a brand new regiment of scaliforms which was called the 'Pindap' regiment. It had the same vertices as the grand antiprism, but was a derivative of the sishi regiment. There's also one with a convex verf, but with fewer edges. But even more exciting were the discovery of two new uniform polychora in this regiment - pecuexdap and pecuexidfap, now the count is at 1855.

November 6, 2020 - _Geometer found a new scaliform named 'starphap'. I suspected an interesting possibility with it and seen it was a part of an infinite category of scaliforms - Category SA - the Hemiantiprisms. I also started listing scaliform padohis to my spreadsheet. On the 10th, I seen that there was 18 scaliform padohis and 59 fissary scaliforms, same with gidipthi scaliforms.

November 11-20, 2020 - I found the first three scaliform dattady members, this category is now official. I started up a regiment map for dattady under kisispic symmetry. Meanwhile, _Geometer found a new scaliform - hog dhidicup. On the 13th, I started listing out the dattadies in search of new scaliforms. My count was finished on the 18th, there are 17 scaliforms and 45 fissary scaliforms there. On the 20th _Geometer found a new scaliform - hocucup.

December 4, 2020 - _Geometer found two new scaliforms which were facetings of diminishings of sidtaxhi and gadtaxady. These had 480 trips and 120 quistets for cells and have ixitic symmetry. He also found an isogonal gyro diminishing of pedip. Things grew a bit quiet after this point - until...

January 28, 2021 - _Geometer found many scaliforms in the disdi regiment (rappisdi regiment with more edges), thus leading to a new scaliform category. He then found 12 uniforms in this regiment, making the count go up to 1867. I investigated the new finds using Stella and seen that they worked, but not only that, there were hords of these things. I first counted 439 which was reduced to 243 due to the number of ways ico regiment members could blend with the core member - siggissido. This officially lead to Uniform Cateogry 30: the Idtessids. I coined the name as a play of the words idcossid and tessic symmetry. The uniform polychoron count now jumped to 2098. This regiment is now the largest polychoron regiment and has demitessic or kidemitessic symmetry depending on member of regiment. After blending rappisdi with this regiment, leading to a second core - siggisdah, 29 more polychora were added, now the count jumped to 2127. I noticed on Feb. 3, that I missed five in the idtessid count, which lead the uniform count to 2132.

February 9, 2021 - _Geometer found a couple of new idtessid members which lead to cores 3 and 4 as well as a fissary and compound idtessid. I explored these new cores which lead to 30 new idtessids leading to a count of 2162. I also found some overlooked ones which added 32 more. Uniform polychoron count is at 2194.

February 16-19, 2021 - More scaliforms were found by _Geometer including one in the 10-sishi regiment. On the 19th, three more scaliform categories were added - S24-S26, Decasishi Scaliforms, Bidex Sishi Derivatives, and Bhidhi Army. These are brotayued by _Geometer.

February 22, 2021 - I coined short names for the 11 swirl symmetry families: Swirldoic, skidoic, scubic, skicubic, ascubic, askicubic, spyritic, stettic, skitettic, astettic, and askitettic.

March 3, 2021 - _Geometer found a new scaliform in the ex regiment as well as it's gishi regiment conjugate. He also made an edge map of the disdi regiment.

March 14, 2021 - _Geometer found some new scaliforms which I then investigated, this lead to category S27 - Octicoes which has 64 members and 44 compounds.

March 16, 2021 - _Geometer found four new idtessids from a 5th core, bringing the total to 2198.

March 23, 2021 - After writing out all possible cells and faces for uniform idtessids, I found out there should only be five cores plus two fissary cores as well as four more cores which lead to only compounds.

April 3, 2021 - I came up with a naming scheme for the idtessids and seen that ten of the ones I had listed crash due to four at a ridge situations. The uniform count drops to 2188 of which 333 are idtessids.

April 21, 2021 - _Geometer found four more scaliforms and these are odd looking, two are from padohi and gidipthi diminishings with sispic symmetry and the others are blends of twelve of each with hyic symmetry which are hollow, their names are sispaxthiccudy, gispaxthiccudy, siddapsiddip sidducstwy, and giddapsiddip sidducstwy. Pondering the possibilities of rissid scaliforms with sispic symmetry, I noticed an amazing possibility to blend rissids containing dip or stiddip with one distadedip verf to the verf and formed a new uniform polychoron in the rissidtixhi regiment with sisp symmetry and there appears to be 28 plus 2 fissaries here - enough to create a new uniform polychoron category - Category 31: Rissid Swirlprisms. Polychoron count is now 2216. There should also be a scaliform cateogry also Category S28: Scaliform Rissid Swirlprisms. The next morning after following a lead by _Geometer on blending these in a certain way, Spirit Backup and myself both found some horrific uniform blends that are as complex as gadros daskydox, these could form an enormous regiment and lead to category 32. We soon figured that cat. 32 was biform and the next day I proved that cat. 31 was biform also, even if their vertex figures are the same at each vertex. These are also called pseudo-uniform, or should we call them 'troll uniforms'.

April 28, 2021 - I checked to make sure the idtessids were uniform under demitessic symmetry, but instead noticed that they are uniform under tessipyritic symmetry. I then realized that there will be several uniform compounds of 2-idtessids. Each tessipyritic one will generate a tessic 2-compound and every kidemitessic one will create two compounds of 2-idtessids, one with demitessic symmetry and the other with kitessic symmetry.

May 9, 2021 - Discord was active in finding all sorts of polychoron alterprisms in 5-D which appear to be scaliform, possibly even an idcossid based one. _Geometer also listed subsymmetric fissary jak facetings. I also considered adding a category S28 - Diminishings and Friends to include those miscellaneous diminishings found by _Geometer earlier.


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